- Email: [email protected]
Spectroscopic information on 36Cl from the (d,p) reaction
Nuclear Physics A481 (1988) 269-293 North-Holland, Amsterdam
SPECTROSCOPIC
INFORMATION
S. PISKOR,
P. FRANC,
ON 36CI FROM
W. SCHAFERLINGOVA
THE (d,p)
REACTION
and J. KREMENEK
Nuclear Physics Institute, 250 68 dei, Czechoslovakia Received
28 September
1987
The reaction 35Cl(d, P)~‘CI was studied at deuteron energy 12.3 MeV using a multi-angle magnetic spectrograph with resolving power E/AE =2000. Precise excitation energies of 77 states in %I up to 7 MeV are presented. The level energies of some states were measured with a precision of 70-80 eV; several new states were found. Angular distributions of proton groups corresponding to 51 states in ‘6CI were analysed using DWBA calculations. Transferred orbital angular momenta and absolute values of spectroscopic factors were deduced. Spectroscopic factors for 36 states are given for the first time. The substantial parts of single-particle strengths for If and 2p orbits are exhausted by the observed I = 3 and I= 1 transitions. Spectroscopic strengths for the positive-parity states show that 2s and Id orbits in the ground state of 35Cl are much more empty than should follow from simple-shell-model or from calculations made in the full space of sd-shell-model wave functions by Wildenthal et al.
Abstract:
E
NUCLEAR
REACTIONS 35Cl(d, p), E = 12.3 MeV; measured Q, a(0). levels, L, J, z-, spectroscopic factors. Natural targets.
36CI deduced
1. Introduction The nucleus 36C1 has been investigated previously with different types of pick-up and stripping reactions and with thermal neutron capture y-ray measurements. The article by Endt and Van der Leun’) reviews the experimental material up to about June, 1978. Let us refer to some papers that are the most related to the present study. Hoogenboom et al. ‘) reported results of PWBA analysis for forty-three states of 36C1 up to 6.7 MeV obtained in the (d, p) reaction at deuteron energy of 7.5 MeV. Spectroscopic factors and I-values for 15 low-lying states of 36C1 observed in the (d, p) reaction at deuteron energy of 7 MeV were reported by Decowski ‘). The paper by Rice et al. “) provides an accurate set of excitation energies, pick-up spectroscopic factors and I-values for states of 36Cl below 8.2 MeV, populated in the (p, d) reaction. Energy levels of 36C1 and some spin assignments were reported by Spits and Kopecky ‘) as obtained from thermal neutron capture y-ray measurements with polarized and non-polarized neutrons. Results of calculations made in the full space of sd-shell-model wave functions for positive-parity states in the nuclei A = 34 - 38 were reported by Wildenthal et al. “). Since the review of Endt and Van der Leun, data on 36C1 have been augmented by Bhat et al. ‘) who measured (d, t) reaction, by Stelts et al. *), by Kennett et al. 9), 03759474/88/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
3. PiskoP et al. / 36Cl
270
by Krusche Calculations
et al. lo) and by Kessler
et al. ‘I) as resulting
in the 2~,,~ - Id,,, - lf,,* - 2p,,,
appeared in print. We have performed
high-resolution
shell-model
measurements
from (n, 7) measurements. space by Hasper 12) have
of the 35Cl(d, P)~~C~ reaction
using the cyclotron at the Nuclear Physics Institute of Czechoslovak Academy of Sciences at Rei. The aim of this paper is to provide a set of precise and accurate energy levels of 36C1, populated in this single-particle transfer reaction and to yield a more complete set of spectroscopic factors as well as new or revised assignments for 1. 2. Experimental 2.1. DATA
procedures and methods of data analysis
ACQUISITION
The 35Cl(d, P)~~C~ reaction was studied at an incident energy of 12.3 MeV. The cyclotron beam of deuterons was momentum separated by means of 100” analysing magnet and focused onto the target. The multi-angle magnetic spectrograph 13), giving in a single run eleven spectra in the range from O”-90” reaction angle, was used for the momentum analysis of the protons. Two natural chlorine targets consisting of 50 pg/cm’ thick layers of CdCl, evaporated on 10 pg/cm2 carbon backings were employed. Two runs with different orientations of the spectrograph with respect to the beam direction were performed with each target. The exposure in each run was 1500 PC. The overall resolving power E/AE achieved with these targets amounted to about 2000. The detection of protons was accomplished by means of 700 mm long nuclear emulsion plates Ilford L4, located in the focal planes of the spectrograph channels. Teflon-coated aluminium absorbers were used to remove the heavier products of competing reactions. Plates were scanned by an automatic scanner i4) and resulting spectra were analysed by means of a code 15) finding the peak positions as well as the number of tracks in spectral lines and providing the corresponding error estimates. A part of a typical proton spectrum is displayed in fig. 1. Elastically scattered deuterons were measured with the same experimental set-up at olab = 10” and &,, = 20” reaction 2.2. IDENTIFICATION,
CALIBRATION
angles. AND
ENERGY
EVALUATION
Targets used in our experiments contained some amount of admixtures, namely H, C, N, 0, Na, Si, S, Cd and 37C1. To facilitate the analysis of the complex proton spectra we processed eleven additional spectra from (d, p) reaction on 100 +g/cm2 Si02 target, taken with the same experimental set-up. These additional spectra, along with kinematical shifts of spectral lines with reaction angle, crosschecked the correct identification of spectral lines. Unambiguously identified singlets
Rcactiol 0.50
1
Angle (deg)
t
Distance along PIate Reaction Angle (deg) 1.25
1.50
470
480 Distance along Plate (mm)
490
Reaction Anglc(drg) 2.25
2.00
‘I
Fig. 1. Proton spectrum from the (d, p) reaction on the CdCI, target, taken near the zero angle. Levels of 36Cl are labelled by the final nucleus symbol and corresponding excitation energy in keV. Impurity lines are marked with the final nucleus symbol only.
Reaction Angle (deg) 3.00
3.25 %
n a
4
E
F a “n
2.15
3 z “,
f 2
8 !$
410
400
z
f
H
%
420
Distance along Plate (mm)
4.00
f
Reaction Angle (deg) 3.15
3.50
I
n
Distance
alongPlate
(mm)
Reaction Angle(deg)
4.25
5.00
330
340 Distance
350 along Platc(nm)
Fig. l-continued
360
3. Piskor'et al. / 36CI with the best known calibration
of spectra
processing possible,
A-values
procedures as many
taken
273
and their error estimates in all spectrograph
adequate
were used for simultaneous
channels
in this respect were described
as 80 calibration
points
in each run. elsewhere
were used to calibrate
The data 16). Where
each particular
spectrum. The (d, p) reaction Q-values used for calibration were derived from the following sources: (i) The neutron binding energies for all nuclei in question from ref. “). (ii) The excitation energies of 13C and 14C from ref. Is), of “N from refs. ‘*,“), of “0 from ref. 19), of 29Si and 3oSi from refs. lv2’), of 31Si, 33S, 35S and 38Cl from ref. ‘), and of 36C1 - the averaged values from refs. 5,9,*o). In deriving the final set of 36C1 excitation energies we included in the analysis fifty-two proton spectra from several runs with different targets containing chlorine as well as CdS targets with chlorine as an impurity.
2.3. DETERMINATION SECTIONS
AND
OF ABSOLUTE TESTING
DIFFERENTIAL
OF OPTICAL-MODEL
CROSS PARAMETERS
Correct evaluation of spectroscopic factors depends on the absolute normalization of the cross section data, on the choice of optical-model parameters, on the boundstate potential well parameters, and on finite-range and non-locality corrections. In table 1 are listed parameters of optical potentials, which are in the given case expected to describe adequately the elastic scattering of particles in entrance and exit channels. In fig. 2 is displayed the angular distribution of u/uR, the ratio of the deuteron elastic scattering cross section to the Rutherford one. The dashed line represents the average
of experimental
data on elastic scattering
of deuterons
by nuclei
in the
mass region from 28 to 40, obtained at deuteron energy of about 12 MeV [refs. 2’*24*25,27,28)]. The dashed area is defined by envelope lines of a/aR curves, calculated with fourteen sets of deuteron optical-model parameters from table 1. The solid curve is the optical-model calculation using parameter set 1 of table 1. In our experiments the chlorine targets of natural abundance were used, i.e. containing 75.77% of 35Cl and 24.23% of 37C1. The target thickness and therefore the absolute cross section was calibrated at &,, = 21” by putting the deuteron elastic scattering cross section u equal to 0.78 ua. Such normalization of absolute cross section is believed to be accurate within about 10%. In fig. 3 are presented the results of DWBA calculations for 1.951 MeV (I = 3), 3.332 MeV (I = I), and 6.085 MeV (I = 1) states with different sets of optical-model parameters, listed in table 1. The calculations have been performed including finite-range and non-locality corrections (FRNL) and also without such corrections (ZRL). The areas in fig. 3 dashed as represented by symbols A and B are defined by envelope lines for the curves of gF&,( 0) and aFRNL nWBA(e), respectively, calculated
3. Piskor'et al. / 36Cl
214
TABLE
Optical b
Set
(MIV)
(Ee$)
w, ‘) (MeV)
potential
1
parameters
(z:V)
rs.0. (fm)
(f?)
Deuterons “)
13 2’) 3 ‘) 4s) 5? 6 ‘) 7j) 8 ‘) 9’) 10 “) 11”) 12”) 13 0) 14’) Protons ‘) I ‘) II “) III ‘)
106.2 107.4 100.6 103.1 102.5 103.0 101.1 109.7 89.9 91.6 112.0 114.6 105.3 56.6
51.4 46.6 50.7
0.188
11.24 9.84 10.20 9.90 9.90 10.50 11.40 10.30 12.33 8.88 18.00 16.20
7.43 7.00 6.00 6.00 6.00 8.00 8.50 8.16 6.97 9.60
0.842 0.860 0.815 0.799 0.813 0.805 0.882 0.809 0.730 0.722 0.900 0.833 0.860 0.928
0.628 0.640 0.666 0.611 0.635 0.580 0.570 0.596 0.744 0.773 0.470 0.548 0.570 0.499
0.583 0.500 0.815 0.799 0.813 0.805 0.600 0.809 0.660 0.722
1.051 1.030 1.070 1.070 1.070 1.070 1.088 1.031 1.170 1.164 1.000 0.995 1.050 1.116
1.553 1.590 1.490 1.530 1.540 1.560 1.562 1.508 1.325 1.374 1.550 1.410 1.510 1.494
0.894 0.750 1.070 1.070 1.070 1.070 0.987 1.031 1.070 1.164
6.20 7.50 8.00
0.750 0.650 0.650
0.549 0.470 0.470
0.750 0.470 0.650
1.170 1.250 1.200
1.320 1.250 1.250
1.010 1.250 1.200
16.70 14.05
1.368
7.81 13.50 11.00
“) All sets have rc. = 1.3 fm. Non-local correction factor p = 0.54. b, W # 0, volume absorption. ‘) W, # 0, surface absorption. d, Parameters derived from those given by Abegg and Datta ‘I), set 1, employing the formulae of ref. 2z), i.e. V, = V,,+0.25(E0-
E,)-2.3(Zo/A;‘3-Z,/A;‘3),
rw, = r,o-0.9(A,“3-A;“3), a,, = a,, -0.082(A;‘3
- A;“)
The subscript 0 refers to the parameters given by Abegg and Datta, whereas the subscript 1 refers to corrected. ‘) 37CI, 12.0 MeV ref. 24). ‘) ?a, 11.8 MeV, ref. 23). those p, 40Ca, 11.8 MeV, ref. 23). “) 38Ar 11.8 MeV ref. 23). ‘)’ Systematics 11.8 MeV, ref. *5). ‘) 39K, 12.8 MeV, ref. 23). k, Ca, 11.8 MdV, ref. 23).‘1) Global potential 26). “) ‘%a, 12.8 MeV, ref. 23). p, 3’P, 12.0 MeV, ref. *3). “) so called “av Z” potential “). “) %a, 12.0 MeV, ref.23). ‘) Ca, 12.1 MeV, ref. 23). ‘) Non-local correction factor p = 0.85. Parameters given for the ground state transition only. ‘) Systematics by Becchetti and Greenlees *9), rc = 1.3 fm. “) Systematics by Perey 30), r, = 1.25 fm. ‘) Modified Perey potential 27), rc = 1.25 fm.
with fourteen sets of deuteron optical-model parameters in the entrance channel (sets 1 to 14 in table 1) and with one set of proton optical-model parameters in the exit channel (set I in table 1). In fig. 3 are also plotted DWBA cross sections calculated with the set 11 of the deuteron optical-model parameters in the entrance channel and with three sets of proton optical-model parameters in the exit channel, i.e. the solid, dashed and dotted curves correspond to cross sections ~~!$aA(‘ti), calculated with sets I, II and III, respectively. In all cases the shapes of angular distributions are very similar. From the analysis of &vBA( O,,,,,) and &i$&( &,,,,),
3. Fiskoi
0.1 I
0
1
I
20
I
et al. I
I
40
275
36Cl
I
1
60
I
I
80 0
Fig. 2. The angular distribution of relative deuteron elastic scattering cross section o/uR. The dashed The optical model calculations with curve is the average of compiled experimental data 21324~25327~28). parameter sets 1 through 14 (table I), all lay within the dashed area. The full-line curve is the opticai model calculation using parameter set 1. Points are our measurements (point at O,, = 21” was used for calibration of absolute cross sections by putting CT/-~ at this angle to 0.78).
calculated with different sets of optical-model parameters, overall conclusions can be made: the sample standard deviations of cross sections in the maxima for the parameter sets of table 1 in the entrance (exit) channels are 8.7% (6..5%), 7.6% (4.4%) and 7.1% (3.8%), while the mean values of a(&,,) suit the approximate relations
for the 1.951 MeV (f = 3), 3.332 MeV (I = 1) and 6.085 MeV (I = 1) states, respectively.
2.4. DWBA
ANALYSIS
A DWBA analysis of angular distributions was performed using the zero-range code DWUCK 31). The bound-state wave function of the transferred neutron was generated using the standard “well depth” routine in which the depth of a singleparticle potential of a fixed Woods-Saxon geometry (r, = 1.25 fm, a, = 0.65 fm) is varied until the single-particle state with given quantum numbers obtains the proper binding energy. The usual factor h = 25 was used in the Thomas spin-orbit term of
20
40
60 80
0
20
40
60
I
I
0
20
il
I
40
Q c. ,“”
I
1
(deg)
j--3/2
I,:
E x= 6084.84
35Cl(d,p)36CI
Fig. 3. Results of DWBA calculations of single-particle cross sections for three %I states, performed with different sets of optical potentials from table 1. The solid, dashed and dotted curves are zero-range and local calculations with set 11 in the entrance channel and sets I, II and III in the exit channel, respectively. DWBA curves calculated with parameter sets 1 through 14 in the entrance channel and set I in the exit channel performed both with finite-range and non-locality corrections and without such corrections all lay within the areas dashed as A and as B, respectively.
0
1.C
1.C
Ex:3332.29
1oc
10I-
-
35CW,p)36CI
IC
lo(
3. Piskor'et al. / 3bCl the same geometry. the calculations. non-locality
The finite-range
The finite-range
correction
factors
and non-locality parameter
for the deuteron
277
corrections
was taken
were included
to be equal
and proton
optical
in
to 0.621. The potentials
were
taken 0.54 and 0.85, respectively. Present DWBA calculations were performed with optical-model potential parameters given in table 1, namely with the set 1 for the entrance channel and with the set I for the exit one. Spectroscopic factors were found by the least-square method of fitting of the theoretical cross sections in the vicinity of the main maxima to the experimental ones, related by
where Ji and Jr are the total angular momenta of the initial and final states, respectively, j represents the total angular momentum transferred by the neutron, SIJ are the spectroscopic factors (fitting parameters), and al,j are the cross sections calculated by DWUCK. Because the target nucleus has non-zero spin, namely J: equals z’, the angular momentum of the transferred neutron is vector-wise added to it, giving the total momentum of the final state. Therefore in some cases two orbital momenta of the transferred neutron, differing in two units, are allowed as well as two different spin orientations for each 1. Because the shapes of angular distributions in single-nucleon transfers are practically dependent on 1 only, experimentally no distinction can be made between transfers with different spin orientations. For this reason only the most probable final single-neutron states are considered, i.e. the 2~,,~, Id,,, and lf,,2 states for 1= I,1 = 2 and I= 3 transfers, respectively, and therefore only the corresponding spectroscopic factors are given. The experimentally observed angular distributions fitted with the DWBA curves are presented in fig. 4. 3. Results and discussion 3.1. ENERGY
LEVELS
OF %I
As should be expected the odd-odd nucleus 36C1 has a very complicated level scheme. Seventy-seven excited states of this nucleus up to 7 MeV excitation energy have been identified in our spectra. In table 2 the excitation energies of the 36C1 levels, found out in the present investigation, are listed together with those from ‘*‘*‘“)] and (p, d) [ref. “)I reactions. (n, Y) [refs. The bulk of today’s most precise data on excitation energies of nuclei or on their neutron binding energies are derived from (n, y) experiments. This is also true for the nucleus 36Cl and as we have used the 35Cl(n, Y)~%ZI data for calibration of our spectra too, let us look at them in more detail. From the thermal neutron capture experiments 5*9,10)extensive sets of spectral components of gamma transitions with high precision quoted are reported, but the data still lack consistency in many points.
3. Piskoi: et al. / ‘6Cl
278
E=788.25 _ 1.0 2 E 2 6 -0
0.1
0
20
40
60
00
0
7
t
E=lb01.41 I=0 j=l/2
20
40
bO
t
E31951.18
I
l=1+3
80
0
20
40
LO
E=1959.16
j=3/2*7/2
1.0
t
0.1
L 80
IQ I
0
20
40
b0
1 80
20
40
60
80
E12467.92
0.1
0
20
40
60
80
0
t
0
20
40
60
I Bern
Fig. 4. Angular distributions of protons from the 35Cl(d , P)~~C~ reaction at E, = 12.3 MeV. The curves are the results of DWBA analysis with finite-range and non-locality corrections included. In cases when the incoherent sum of two I transfers was fitted, both components are also displayed.
279
3. Piskoi et al. / 36CI
r-----E'2863.61
d
xb
I=2
1.0
j.312
-0
1.0
0.1
I
0
IIY.Ih 0 20
.
20
UO
60
10.01
I
40
0
60
20
40
60
1 E=2994.86
:
1
0 1
10.0:
E=3332.29
Es3207.35
t
t
20
40
60
j
:
E=3634.99
: 1.0:
Ea3723.40 I=3
c
0
20
40
60
00
0
20
40
Fig. 4-continued
60
80
0
20
40
60
80
3. Piskoi er al. / %2I
280 7
7
c
10.0:
E=3962.63
0
20
40
60
E=403l.98
1BO
0
20
60
40
0
t
I
40
t
E=4060.53
I=1
1.0:
20
60
I
E'4315.66
I-,
I=1
I=1
1.0
i=3/2
I
2
10.0:
10.0: E=4496.31
0
20
40
60
E=4551.66
80
0
20
40
60
E14598.56
80
0
20
40
60
80
4.m
Fig. 4-continued
:
3. Piskoi et 3
‘=
< 2
E=U753.83
2
1=1+3
0
20
40
60
1
j
t
4
E=4956.47
E=4997.82
I=1
80
F
0
20
40
60
E=5079.18
1=1+3
80 -3
I
t
281
al. / ‘6CI
0
20
E=5204.85
1'1
1.0:
80
80 7 lO.Or------
7
i
0
20
I
20
40
60
i BO
1
0
20
40
Fig. 4-continued
60
40
60
10.0
E=5308.12
0
80
60
10.01
E=5150.40
t
40
E=5463.43
80
0
20
40
60
80 8 cm
3. Piskor’
282
et al. f 36C1
_~-_- .- _ 10.0 E=S619.23
:
4 I." f
0
20
60
80
0
20
UO
60
80
u
a0
0
E"5831.94
t
F
40
.
E=6051.09 1.0 i=UZ+tn
1.0
0.1 0.1
0
20
40
60
I
I
0
20
40
Fig. P-continued
60
I
80
~ 0
20
40
b0
I
3. Piskoi et al. / 36CI
283
T Ee6253.58
0
20
40
60
E36504.60
80
0
20
40
60
80
0
-I 80
20
40
60
20
40
60
7
E=6576.67 I=1 i=3/2
\
0
20
40
60
80
1
0
20
I
40
60
80
0
;
@cm Fig. 4-continued
Spits and Kopecky ‘) reported 420 gamma rays, from which 236 were placed in a 36C1 decay scheme between 72 bound states. Kennett et al. “) assigned 201 gamma rays from the total number of 234 observed ones as being transitions between 64 states of 36C1. By Krusche et al. lo) 236 transitions out of 398 ones, attributed to the reaction 35Cl(n, Y)~?J, were placed in their level scheme of 36C1, consisting of 74 states. In fig. 5 are displayed energy distributions of transitions from the above-mentioned (n, y) experiments. The histograms dashed as represented by symbols A, B and C correspond to data by Krusche et al.lo), by Spits and Kopecky 5, and by Kennett etal.9),respectively. Very surprising in this picture is the low overlap of these three gamma transition sets and also that in these three papers only about 50% of the overlapping transitions are assigned as transitions between the same set of energy levels of 36C1 - see the histogram dashed D type.
s. Piskor’ et al. / 36Cl
284
TABLE Levels
of %I
below
7.0 MeV excitation
and as compiled
2
energy
from previous
as observed in the present measurements
study
E,(keV (4
P) “) 0
(n, Y) “)
(P. d) ‘)
0
J” d,
0
2+
788.444*0.016
789&l
3+
1165.13*0.28
1164.888+0.013
1165*1
1601.41 kO.95
1601.113*0.021
1600*
1951.18kO.49
1951.198*0.020
1959.16*0.29
1959.410*0.013
195851
2+
2467.92 f 0.36
2468.281 *to.028
2467 * 2
3-
2492.33 f 0.45
2492.321*
0.021
2491*2
2+
2518.47k0.14
2518.420+
0.024
2517*2
5-
2675 f 2
1+ (2fS)i
788.25 * 0.48
2676.O;t 1.1 2810.95kO.19
1+ 1
1+ 2-
2676.421 zt 0.041 2810.604*0.038
2863.61 f 0.82
2863.957 * 0.028
2863 * 2
2896.45 * 0.09
2896.342 * 0.026
2894*2
2994.86 f 0.14
2994.691 f 0.034
2995 f 2
(2,3)_ (l-3)_
3099.75 *0.40
3100.724*0.045 3208 * 4
(0-3)_
3207.35 i 0.20 3332.29 f 0.07
4-
3208.62 f 0.29 ‘) 3332.314 f 0.034
3331 i3
3469.1 zt 1.3
3470.036*
3470*
3600.2 f 1.3
3599.549 * 0.036
3634.99 * 0.15
3634.992 * 0.094
0.063
23
(1,2)+
3598 f 3
(1,2)+ 3-
(3661)
(1 -f;+,
3722iz4
4-
3566+4
3663.0+
1.4
3660.494 * 0.190
3723.40 f 0.38 3825.9*
1.7 (1 -4)+
3830.518 *to.425 ‘) 3941.290i0.185 3962.63 * 0.11 3992.06 + 0.08
h,
(l-3)+ 3962 f 4
3962.831 *to.103 3992.40 * 0.21 ‘)
(1 -3)_
4030*
(1,2)_ (O-3)_
3997.553 f 0.294 ‘) 4031.98iO.09
4031.971*0.187
4060.53 f 0.79
4061.473*0.127
4138.8OkO.18
4138.951 kO.118 4205.64OkO.185
4262.0*
1.8
4293.0*
1.8
(2,3)_ h,
4315.60*0.30g) 4410.044*0.216
4496.31*0.12
(1,2)Y 5
h,
4299.700 * 0.211 h) 4315.66+0.17 4405.6 f 1.5
2-
3990 * 4
4205 f 4
(1,2)+
4299 * 3
O+,T=2
4316*4 h,
(O-3)_ (l-3)’
4496.686 * 0.172
2-
4525.235 * 0.145
4524k4
4551.66*0.59
4551.504*0.176
4551*4
4598.56 * 0.09
4598.449*0.173
2+ (1,2)+ 3-
4720 * 4 4724.1 zt 1.5 4738 + 5 4753.83 kO.27
4754.222 * 0.178 ‘)
(2,3)_
3. Piskor'et al. / 36Cl TABLE
285
2-continued
-WkeV) (4 P) “1
(4 Y) “1
(P,4 ‘1
4757.969 f 0.123
J" d, 3-
4823.7 f 1.5 4829.563 +0.148 4843.219kO.294’)
4s30* 5
(1 -4)+
4852 1-4
(2,3)_
4884*4 4953 f 5
(1, a+
4846.7 * 1.5 4876.7 f 1.5 4883.95 f 0.85 4956.47 f 0.33 4997.82*0.16 5079.18 f- 0.50
(O-3)_ 4997.390 f 0.220 5018.115+0.066 5079.169kO.158
(2,3)(1 -4)+ (l-3)_ 5144*6
5150.40*0.47 5204.85 f 0.20
5150.686*0.118 5204.654* 0.123 5246.692 f 0.143
5263.12kO.10 5308.12*0.11
5263.123 zkO.175
(2,3)_ (l-3)’ 5249 f 5
5329.178*0.128 5332.5 f 1.5 (5369.8 * 1.5)“Cl 5463.43 f 0.08
5463.515*0.125 5473.709*0.161
(2,3)_ (l-3)_
(2,3)_ (1,2)_ (l-3)_ (o-3)+
(1,2)_ (o-3)+
h,
5512.8* 1.5 5517.747*0.107
5517*5
3-
5545.0* 1.5 5578.31 f 0.22
5563.633 +0.130 5578.500*0.115 5604.467 f 0.134
5605 * 5
5619.23 + 0.09 5694.42 * 0.21 5703.152iO.138 5734.116*0.129 5778.304i 0.232
5702 l 5 5734*6
5831.94*0.38 5866.6* 1.5 5898.48 kO.10 5912.01*0.11
(2-, 3) 22+ (O-3)_ (O-3)_ (2,3)_ (2,3)_ (l+-3) (O-3)_ (O-3)_ (O-3)_
5913*5
(1,2)+
5957*5
(1,2)+
5986 f 5
(2,3)_ (2,3)+ (O-3)_
5947.6 + 1.5 5956.762 f 0.142 5967.6 f 1.5
6051.09*0.31 6084.84 * 0.08 6089.883 f 0.207 g)
(2,3)_ (l-3)
s. fiskor’ et al. / 36CI
286
TABLE 2-continued
ESkeV) (4 Y) 9
(4 P) “)
6184.95510.151 6236.41 f 0.53 6253.58rtO.13 6268.34 * 0.75 6340.35 f 0.26
(P, d) ‘) 6095 f 5 6146*5 6184*5
r)
6253.734*0.180’) 6268.398* 0.152 6340.020 f 0.254 ‘) 6344.350+0.163 6354.930 * 0.190 ‘) 6379.547 kO.131 6423.483 f 0.152
6354*6 6379 f 5 6423 f 5 6480 f 7
6487.739ztO.159 6504.60 f 0.47 6528.43 * 0.50 6538.210*0.213
h,
J”“) (1,2)’ (1,2)’ (1,2)’ (2,3) 2(2X-4’) (l-3)_ (1.2)’ (1.2)’ (1,2)’ (2.3) (2,3)(l-3) (2,3)Y (l-3)
6539.8 * 1.5 6545.032ztO.138 6550* 5 6576.67 * 0.50 6595.18 f 0.78 6604.57 * 0.64
6596 f 7 6604.380*0.213
h, 661855
6642.752kO.157 6673.13 kO.15
6773.207 f 0.185 h,
(l-3) (I, 2)+ (O-3)_ (2,3)Y (l-3) (O-4)’ l_
6683 i 5 6750*6 6774 f 6 6826*6
(2,3)Y (2,3)Y (1,2)+ (o-4)+ (o-4)+
6893 f 7
(l-3) (1,2)+
6836.521 kO.203 “) 6950.02 * 0.7 1 6952.404 f 0.241
(I-3) (O-3)_
6997.14kO.21
“) Present work. States with quoted errors exceeding one keV are weakly populated in the (d, p) reaction and their assignment to %Zl nucleus is probable but not certain. ‘) The weighted average of three (n, y) measurements sS9,‘a). The quoted errors are those of weighted means multiplied by the overall consistency factor 2.64 for the whole set of (n, y) states or by the local consistency factor for each particular state, whichever is greater. The consistency factors 34) are defined as follows F,=(l/(n,-1)
:
((E;-E;,)2/u;))“*
the local consistency
factor,
j=1
F=(l/(N-M)
c” 2 ((E,-E,)*/a2,))“’ I=1 j-1
the overall
consistency
factor
3. Piskor'et al. / 36CI
287
TABLE 2-continued where index j denotes different measurements (n-number of authors) and index i denotes different states (M-total number of states, N =C,“_, n, total number of measurements). Twelve of the states reported by Spits and Kopecky ‘), not confirmed by Kennett et al. ‘) and by Krusche et al. lo), are not included in the table. For reliability and consistency of (n, y) data see text. ‘) From ref. 4). d, Spin-parity assignments from ref. I), from the present work and from the application of recommended upper limits 32) to the y-ray strengths computed from the y-ray branchings 5.9,‘o) and lifetimes I). “) ‘) s) Not ‘) ‘)
Reported in refs. 5.9), but not in ref. lo). Reported in refs. 9,‘o), but not in ref. 5). Reported in refs. ‘,t’), but based on different reported in ref. ‘). Reported in ref. lo) only. Reported in ref. 9, only.
2000
4000
transitions.
6000
8000
E, keV
Fig. 5. Histograms representing the energy distributions of measured gamma transitions from three different (n, y) experiments. The histograms dashed as A, B and C are results of papers by Krusche et al. lo), by Spits and Kopecky 5, and by Kennett et al. 9), respectively. The histogram dashed as D represents the number of transitions to which in all three papers the same interpretation was given.
3. Piskoi et al. 1 36Cl
288
In deriving which
errors
are presented
overall consistency
of averaged
excitation
energies
from the (n, y) experiments,
column
of table
2, for 54 common
in the second
factor 2.64 was necessary.
states were much greater,
The local consistency
states the
factors for some
e.g. for the 3100.724 keV state it amounted
to 6.45 (see
table 2, note b). Applying the consistency factors to the final errors, we cannot, unfortunately, take into account the systematic uncertainties, i.e. that the resulting excitation energies of some states are biased due to the fact that though they are based on the same gamma transition sets in all three works, it is possible that some of the transitions are wrongly assigned. Fortunately on the other hand there exists a sufficient number of strongly populated states to which the accurate and precise gamma transitions are probably correctly assigned, though some small components hidden in strong lines can hardly be distinguished. In any case, the excitation energies based on the Ritz combinational principle only must be taken with caution and more careful analysis of the existing (n, 7) data as well as coincidence measurements seem quite desirable. Most of our new or readjusted energy levels of 36C1 nucleus in the first column of table 2 are believed to be reliable within quoted errors. The reason for this is that we used as many as possible independent calibration data (up to 80 calibration points in about 8 MeV energy interval) in which 36C1 data amounted to 30-40%. Some weakly populated states given in the first column with quoted errors exceeding 1.0 keV are probable but not with certainty established states of 36C1. They were observed with low statistics at few reaction angles only. The set of excitation energies from (p, d) reaction in Rice et al. “) are found to be quite accurate with pessimistic estimates of precision given. This is not the case with (d, p) energies in Hoogenboom et al. ‘) (not presented in table 2) where precision of about 8 keV was quoted and for which differences of more than 10 keV were found. The angular momenta and parities of 36C1 states presented in the last column of table 2 are based on the review article by Endt and Van der Leun ‘) including assignments from the (p, d) reaction 4), on our Z-assignments from the (d, p) reaction and on the application of the recommended upper limits for strengths transitions of given multipolarity 32) to the (n, y) measurements. 3.2. SPECTROSCOPIC
FACTORS,
I- AND
of gamma
r-ASSIGNMENTS
The experimental angular distributions agree quite satisfactorily with the DWBA calculations. In most cases this enabled us to assign unambiguously the transferred orbital angular momenta I to the main components of angular distributions and consequently to derive parities of states in question and to extract the corresponding spectroscopic factors. We have fitted two Z-components in the cases where their presence was evident. Nevertheless, most of the angular distributions, classified in fig. 4 as being pure I = 1 transitions, reveal a typical feature, i.e. that outside the
3. Piskor'et al. / ‘6CI main maxima
the experimental
cross sections
clear if this is due to the possible neutron
transfer,
uncertainties
presence
or if it is an indication
of optical-model
parameters.
289
exceed the theoretical of a small
I= 3 component
of DWBA The point
ones. It is not
limitations
in a given
including
the
is that such a behaviour
I = 1 angular distributions was observed also in some (d, p) experiments in energy and mass region, performed on even-even targets, i.e. where only I-component is allowed, see e.g. 34S(d, p)3sS in Abegg and Datta 2’). So when are quoting the pure Z= 1 component, in some cases the presence of small
of this one we 1= 3
component is possible. Our I-assignments and spectroscopic strengths for states below 3.4 MeV are given in table 3 in comparison with those of Decowski 3, and with theoretical values of spectroscopic strengths calculated in the full space of sd-shell-model wave functions for positive-parity states by Wildenthal et al. “). With the exception of the ground state and 2863.61 keV state transitions the consistency of our data with those by Decowski is quite satisfactory. We can compare neutron stripping spectroscopic strengths given in table 3 with the proton stripping strengths for transitions to the first two analog states in 36Ar (i.e. J” = 2+, T = 1 and J” = 3+, T = 1) observed in the reaction 35C1(3He, d)36Ar by Moinester and Parker Alford 33). Though both neutron stripping values for the transition to the first excited state in 36C1 are in good agreement with the value 2.18, observed in ( 3He, d) reaction, spectroscopic strengths for the transition to the ground state observed in (d, p) experiments exceed significantly the value 3.84 given by Moinester and Parker Alford. From comparison in table 3 of observed (d, p) spectroscopic strengths with those calculated by Wildenthal et al. “) we see that the experimental values exceed considerably the theoretical ones. It should not be surprising as one can expect that due to pairing effects the single-particle orbits with higher orbital momenta, namely the lf7,* orbit for instance, are partly populated in the ground state of 35C1 and therefore sd-orbits are emptier than is expected in the simple sd-shell-model or in the above mentioned as active. The configuration take into account
calculations, space neither
where only Id,,,,
used in the calculations the negative-parity
2s,,* and Id,,, orbits are treated by Wildenthal
states of %l,
et al. allows to
nor some real positive-
parity states, the so-called intruder states, the true eigenfunctions of which are a mixture of pure sd-shell states and even-parity fp-shell distributions. Hasper I*) performed shell-model calculations in augmented configuration space, where also particles in lf,,* and 2p,,, shells were treated as active, though the Id,,, subshell was not included in the model used in his study. Unfortunately from our point of view the 35CI was not calculated by Hasper, i.e. the 35C1 ground-state wave function calculated in the frame of used configuration space is not available. This does not allow us to calculate spectroscopic factors, especially for negative-parity states, and compare them with the experimental ones. Nevertheless, a qualitative comparison is possible.
3. Piskor'et al. / 36Cl
290
TABLE
Values of 1 and (25,+ l)S, for the reaction
(da/do);:
I
3 35Cl(d, P)~‘CI (states below 3.4 MeV)
Experiment
Theory b,
(mb/sr) This work “) 0
788.25 1165.13 1601.41 1951.18 1959.16 2467.92 2492.33 2518.47 2810.95 2863.61 2896.45 2994.86 3099.75 3207.35 3332.29
1.62 0.61 2.64 1.75 1.25 3.28 3.44 1.12 2.66 1.10 0.41 5.50 3.37 0.41 2.07 7.34
032 2 032 0 1,3 0 1,3 092 3 3 2 1,3 1 3 1 1
0.19,5.89 2.23 0.34,0.94 0.22 0.30,3.99 0.39 0.90,4.58 0.12,0.30 10.17 4.08 0.95 1.45,2.05 0.90 1.46 0.53 1.86
Ref. ‘) < 0.07, 8.21 2.03 0.33, 1.03 0.14 -, 4.26 0.53 0.76, 5.37 0.15, 9.32 4.11 4.16 ‘) 1.45, -
2s I/2
Id,/,
ld,,,
0.03 0.19 0.03
3.59 1.33 0.44 0.09
0.01 0.11 0.03 0.02
0.15
0.03
0.13
0.25
0.00
0.15
0.00
0.42
? *) 0.50 1.79
“) Values for I= 0, 1,2,3 are for 2s,,,, 2p,,,, Id,,, and If,,, calculations, respectively. Spectroscopic factors Sj for 2p,,a, Id,,, and lf5,a transitions can be related to those presented by means of the following approximate relations: S,,,,a = (1.15 -0.04 E +0.003 E’)S,,,,,, S,,,,, = S,,,,,/(1.21+0.031 E) E+o.oll E2)S,,,,,, where E is the excitation energy in MeV. and S3.5,2 =(1.54-0.105 b, Average values of calculations made with four different effective hamiltonians in the full space of sd-shell-model wave functions for positive-parity states 6). ‘) Values for 1~3. d, Not measured.
Let us look, e.g., at the state 2863.61 keV. Contrary to Decowski ‘) (as well as to Hoogenboom et al. ‘) we have found the positive parity for this state in accordance with the result of the (p, d) experiment. From (n, y) measurements the possible spin of this state is 2 or 3. Calculations by Wildenthal et al. “) give only three 2+ states in the range up to 4 MeV. Therefore in the frame of their model the state 2863.61 keV could be the second 3+ state originating mainly from the orbit Id,,, (see table 3). In the energy range up to 4 MeV the calculations by Hasper ‘*) give two more 2+ states in comparison with the sd calculations. The possible candidate for the state in question could be the fourth 2+ state at 3.05 MeV with the following main components of wave functions: 53% s-‘dM3 and 17% sP’dP5f2. From a qualitative point of view a relatively strong 1= 0 component should be expected in populating such a state. As is seen from table 3, this state has the pure I = 2 component only. Therefore the 2863.61 keV state should be more probably interpreted as a second 3+ state.
3. Piskoi et al. / 36CI Orbital
angular
momenta
1 and the corresponding
states above 3.4 MeV are presented Orbital
angular
spectroscopic
strengths
for
in table 4.
1 assigned
momenta
291
in PWBA analysis
et al. ‘)
by Hoogenboom
agree in most cases quite satisfactorily with ours. We can check, at least qualitatively, the set of derived spectroscopic factors by applying the sum rules, i.e. that the sum of weighted spectroscopic factors should be equal to the number of neutron holes in the target nucleus in a subshell n, 1,j (or in a subshell n, I- when we do not distinguish between different spin orientations, i.e. between j = 1 +a and j = 1-G orbits). The weights are the well-known statistical factors (2Jr+ 1)/(2Ji + 1) and the summation has to be extended over all the final states (whatever the Jr) which can be reached by transfer of a neutron in the subshell n, 1,j (or in the subshell n, 1). Sums of weighted spectroscopic factors from our experiment are in table 5 compared with those of Decowski 3), with the theoretical ones of Wildenthal et al. “) and with the simple shell-model estimates. According to the note “) below table 3 a slightly smaller value is expected for I= 2, whereas somewhat greater values could appear for I= 1 and I= 3. Values for I= 1 and I= 3 could also be uncertain to some degree due to the already discussed problems, i.e. that some angular distributions considered in our analysis as having a single-l character could be in fact superpositions of two l-components.
TABLE Values of I and (25,+
1)s for the reaction
35CI(d , ~)~%l
4 (states above 3.4 MeV) as observed
in the present
investigation
(du/dfi);:
I
(2J,+l)s,“)
(du/dfl)F: (&
,
(mb/sr)
(25,+
I)%“)
3600.2
0.33
1
0.08
5263.12
3.01
1
0.56
3634.99
1.77
1
0.43
5308.12
2.94
1
0.55
3723.40
0.35
3
1.12
5463.43
4.34
1
0.78
3962.63
2.40
1
0.55
5578.31
0.81
0.11,0.75
3992.06
4.15
1
0.94
5619.23
3.77
1,3 1
403 1.98
3.43
1
0.78
5694.42
0.98
1
0.17
4060.53
0.41
1
0.09
5831.94
0.67
1
0.11
4138.80
1.53
1
0.34
5898.48
3.22
1
0.53
4315.66
1.67
1
0.37
5912.01
2.50
1
0.41
4496.31
4.17
1
0.89
6051.09
0.98
1
4551.66
0.50
0,2 1
0.03,0.33
6084.84
5.97
L3
0.91,0.82
6236.41
0.10,0.67
0.15,0.44
193 1
0.27,0.45
0.25
6253.58 6340.35
0.88 1.92
133
1,3 1
0.24, 1.10
6504.60
2.71
193 1
0.38,0.24
193 1
0.21, 0.38
0.70
4598.56
3.33
4753.83
0.79
4956.47
1.29
4997.82
1.41
5079.18
0.57
1,3 1
0.11
6576.67
1.02
5150.40
0.72
1
0.14
6673.13
1.66
5204.85
2.80
1
0.53
6997.14
1.53
“) See comment
“) below
1.16
table 3.
b, For I = 0, 2 the values of (25,+
l)S, are equal to 0.01 and 0.69, respectively.
0.66
0.16
0.17 0.14 0.20
b)
3. Piskoi et al. / j6CI
292
TABLE
Comparison
of experimental
and theoretical
5
sum rules for neutron 2p orbitals
stripping
into 2s, Id, If and
1 [w,+1)/wi+1)1~, Jr(U I
Experiment Present
Theory
Decowski
a)
Wildenthal
0.31 2.82 b,
0.32 2.66 8.08 4.74
er al. “)
Simple shell-model
0.18 1.61
If and 2p empty, “) 2s filled; Id,,, half-filled; b, Not included states 2863.61 keV (different
i.e. number
I assigned)
“)
0 2.0 14.0 6.0
of holes = 2 (21+ 1). and 4551.66 keV (not measured).
From table 5 we see that the significant parts of If and 2p single-particle are exhausted by states up to 7 MeV observed in our experiment.
strengths
4. Conclusions Excitation energies of 77 states up to 7 MeV were obtained through the 35Cl(d, ~)~%l reaction. Eighteen states; 3207.35, 3723.40, 3992.06, 5308.12, 5619.23, 5694.42, 5831.94, 5898.48, 5912.01, 6051.09, 6084.84, 6236.41, 6504.60, 6528.43, 6576.67, 6596.18, 6673.13 and 6997.14 keV, are new or established with almost two orders higher precision than was quoted in the earlier (d, p) experiments. Eight states: 4031.98,4315.66,4496.31,4598.56,4997.82,5263.12, 5463.43 and 6253.58 keV, were established
with higher
precision
than in the (n, y) experiments.
Precision
of
about 70-80 eV achieved for some strongly populated states is quite unusual in experiments with charged particles. DWBA analysis of angular distributions allowed us to deduce 1 and absolute values of spectroscopic factors for 51 states. Based on I-assignments the spin and parity restrictions were obtained l-assignments are in agreement. for the first time.
for these states. Where J” values are known, our Spectroscopic factors for 36 states were obtained
References 1) 2) 3) 4) 5) 6)
P.M. Endt and C. van der Leun, Nucl. Phys. A310 (1978) 1 A.M. Hoogenboom, E. Kashy and W.W. Buechner, Phys. Rev. 128 (1962) 305 P. Decowski, Nucl. Phys. Al69 (1971) 513; Al96 (1972) 632 (erratum) J.A. Rice, B.H. Wildenthal and B.M. Preedom, Nucl. Phys. A239 (1975) 189 A.M.J. Spits and J. Kopecky, Nucl. Phys. A264 (1976) 63 B.H. Wildenthal, EC. Halbert, J.B. McGrory and T.T.S. Kuo, Phys. Rev. C4 (1971) 1266
3. Piskofet al. / 36CI 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28)
29) 30) 31)
32) 33) 34)
293
C.M. Bhat, N.G. Puttaswamy and J.L. Yntema, J. of Phys. G7 (1981) 1529 M.L. Stelts and R.E. Chrien, Nucl. Instr. Meth. 155 (1978) 253 T.J. Kennett, M.A. Islam and W.V. Prestwich, Can. J. Phys. 59 (1981) 93 B. Krusche, K.P. Lieb, H. Daniel, T. von Egidy, G. Barreau, H.G. Borner, R. Brissot, C. Hofmeyr and R. Rascher, Nucl. Phys. A386 (1982) 245 E.G.Jr. Kessler, G.L. Greene, R.D. Deslates and H.G. Biierner, Phys. Rev. C32 (1985) 374 H. Hasper, Phys. Rev. Cl9 (1979) 1482 P. Franc, J. KIemCnek, S. Piskoi and W. Schaferlingova, Czech. J. Phys. B29 (1979) 1084 R. Batter, J. Kiemtnek, S. Piskoi, Z. Svoboda and V. Skaba, Nucl. Instr. Meth. 157 (1978) 83 V. Kroha and K. Putz, 7th Conf. of Czechoslovak Physicists (Czech. Union of Math. and Phys., Prague, 1981) p. 02-36 P. Franc, J. Kiemenek, S. Piskoi and W. Schaferlingova, Nucl. Instr. Meth. 211 (1983) 159 A. H. Wapstra and G. Audi, Nucl Phys. A432 (1985) 1 F. Ajzenberg-Selove, Nucl. Phys. A360 (1981) 1 F. Ajzenberg-Selove, Nucl. Phys. A375 (1982) 1 T.J. Kennett, W.V. Prestwich, R.J. Tervo and J.S. Tsai, Nucl. Instr. Meth. 215 (1983) 159 R. Abegg and S.K. Datta, Nucl. Phys. A287 (1977) 94 J.A.R. Griffith, M. Irshad, 0. Karban and S. Roman, Nucl. Phys. Al46 (1970) 193 C.M. Perey and F.G. Perey, At. Data Nucl. Data Tables 17 (1976) 1 G.P.A. Berg and P.A. Quin, Nucl. Phys. A274 (1976) 141 W. Fitz, J. Heger, R. Santo and S. Wenneis, Nucl. Phys. Al43 (1970) 113 W.W. Daehnick, J.D. Childs and Z. Vrcelj, Phys. Rev. C21 (1980) 2253 R.H. Bassel, R.M. Drisko, G.R. Satchler, L.L. Lee, Jr., J.P. Schiffer and B. Zeidman, Phys. Rev. 136 (1964) 960 A.N. Vereshchagin, I.N. Korostova, O.F. Nemets, L.S. Sokolov, V.V. Tokarevskii, I.P. Chernov and A.A. Yatis, Elastic scattering of 13.6 MeV deuterons, Institute of Physics of the Ukrainian SSR Academy of Sciences, Kiev (1970) F.D. Becchetti, Jr, and G.W. Greenlees, Phys. Rev. 182 (1969) 1190 F.G. Perey, Phys. Rev. 131 (1963) 745 P.D. Kunz, Instruction for the use of DWUCK: a distorted wave Born approximation program, Univ. Colorado report COO-535-606; Algebra used by DWUCK with applications to the normalization of typical reactions, Univ. Colorado report COO-535-613 (1970) P.M. Endt, At. Data Nucl. Data Tables 23 (1979) 3 M.A. Moinester and W. Parker Alford, Nucl. Phys. Al45 (1970) 143 A.H. Wapstra and N. B. Gove, Nucl. Data Tables 9 (1971)
SPECTROSCOPIC
INFORMATION
S. PISKOR,
P. FRANC,
ON 36CI FROM
W. SCHAFERLINGOVA
THE (d,p)
REACTION
and J. KREMENEK
Nuclear Physics Institute, 250 68 dei, Czechoslovakia Received
28 September
1987
The reaction 35Cl(d, P)~‘CI was studied at deuteron energy 12.3 MeV using a multi-angle magnetic spectrograph with resolving power E/AE =2000. Precise excitation energies of 77 states in %I up to 7 MeV are presented. The level energies of some states were measured with a precision of 70-80 eV; several new states were found. Angular distributions of proton groups corresponding to 51 states in ‘6CI were analysed using DWBA calculations. Transferred orbital angular momenta and absolute values of spectroscopic factors were deduced. Spectroscopic factors for 36 states are given for the first time. The substantial parts of single-particle strengths for If and 2p orbits are exhausted by the observed I = 3 and I= 1 transitions. Spectroscopic strengths for the positive-parity states show that 2s and Id orbits in the ground state of 35Cl are much more empty than should follow from simple-shell-model or from calculations made in the full space of sd-shell-model wave functions by Wildenthal et al.
Abstract:
E
NUCLEAR
REACTIONS 35Cl(d, p), E = 12.3 MeV; measured Q, a(0). levels, L, J, z-, spectroscopic factors. Natural targets.
36CI deduced
1. Introduction The nucleus 36C1 has been investigated previously with different types of pick-up and stripping reactions and with thermal neutron capture y-ray measurements. The article by Endt and Van der Leun’) reviews the experimental material up to about June, 1978. Let us refer to some papers that are the most related to the present study. Hoogenboom et al. ‘) reported results of PWBA analysis for forty-three states of 36C1 up to 6.7 MeV obtained in the (d, p) reaction at deuteron energy of 7.5 MeV. Spectroscopic factors and I-values for 15 low-lying states of 36C1 observed in the (d, p) reaction at deuteron energy of 7 MeV were reported by Decowski ‘). The paper by Rice et al. “) provides an accurate set of excitation energies, pick-up spectroscopic factors and I-values for states of 36Cl below 8.2 MeV, populated in the (p, d) reaction. Energy levels of 36C1 and some spin assignments were reported by Spits and Kopecky ‘) as obtained from thermal neutron capture y-ray measurements with polarized and non-polarized neutrons. Results of calculations made in the full space of sd-shell-model wave functions for positive-parity states in the nuclei A = 34 - 38 were reported by Wildenthal et al. “). Since the review of Endt and Van der Leun, data on 36C1 have been augmented by Bhat et al. ‘) who measured (d, t) reaction, by Stelts et al. *), by Kennett et al. 9), 03759474/88/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
3. PiskoP et al. / 36Cl
270
by Krusche Calculations
et al. lo) and by Kessler
et al. ‘I) as resulting
in the 2~,,~ - Id,,, - lf,,* - 2p,,,
appeared in print. We have performed
high-resolution
shell-model
measurements
from (n, 7) measurements. space by Hasper 12) have
of the 35Cl(d, P)~~C~ reaction
using the cyclotron at the Nuclear Physics Institute of Czechoslovak Academy of Sciences at Rei. The aim of this paper is to provide a set of precise and accurate energy levels of 36C1, populated in this single-particle transfer reaction and to yield a more complete set of spectroscopic factors as well as new or revised assignments for 1. 2. Experimental 2.1. DATA
procedures and methods of data analysis
ACQUISITION
The 35Cl(d, P)~~C~ reaction was studied at an incident energy of 12.3 MeV. The cyclotron beam of deuterons was momentum separated by means of 100” analysing magnet and focused onto the target. The multi-angle magnetic spectrograph 13), giving in a single run eleven spectra in the range from O”-90” reaction angle, was used for the momentum analysis of the protons. Two natural chlorine targets consisting of 50 pg/cm’ thick layers of CdCl, evaporated on 10 pg/cm2 carbon backings were employed. Two runs with different orientations of the spectrograph with respect to the beam direction were performed with each target. The exposure in each run was 1500 PC. The overall resolving power E/AE achieved with these targets amounted to about 2000. The detection of protons was accomplished by means of 700 mm long nuclear emulsion plates Ilford L4, located in the focal planes of the spectrograph channels. Teflon-coated aluminium absorbers were used to remove the heavier products of competing reactions. Plates were scanned by an automatic scanner i4) and resulting spectra were analysed by means of a code 15) finding the peak positions as well as the number of tracks in spectral lines and providing the corresponding error estimates. A part of a typical proton spectrum is displayed in fig. 1. Elastically scattered deuterons were measured with the same experimental set-up at olab = 10” and &,, = 20” reaction 2.2. IDENTIFICATION,
CALIBRATION
angles. AND
ENERGY
EVALUATION
Targets used in our experiments contained some amount of admixtures, namely H, C, N, 0, Na, Si, S, Cd and 37C1. To facilitate the analysis of the complex proton spectra we processed eleven additional spectra from (d, p) reaction on 100 +g/cm2 Si02 target, taken with the same experimental set-up. These additional spectra, along with kinematical shifts of spectral lines with reaction angle, crosschecked the correct identification of spectral lines. Unambiguously identified singlets
Rcactiol 0.50
1
Angle (deg)
t
Distance along PIate Reaction Angle (deg) 1.25
1.50
470
480 Distance along Plate (mm)
490
Reaction Anglc(drg) 2.25
2.00
‘I
Fig. 1. Proton spectrum from the (d, p) reaction on the CdCI, target, taken near the zero angle. Levels of 36Cl are labelled by the final nucleus symbol and corresponding excitation energy in keV. Impurity lines are marked with the final nucleus symbol only.
Reaction Angle (deg) 3.00
3.25 %
n a
4
E
F a “n
2.15
3 z “,
f 2
8 !$
410
400
z
f
H
%
420
Distance along Plate (mm)
4.00
f
Reaction Angle (deg) 3.15
3.50
I
n
Distance
alongPlate
(mm)
Reaction Angle(deg)
4.25
5.00
330
340 Distance
350 along Platc(nm)
Fig. l-continued
360
3. Piskor'et al. / 36CI with the best known calibration
of spectra
processing possible,
A-values
procedures as many
taken
273
and their error estimates in all spectrograph
adequate
were used for simultaneous
channels
in this respect were described
as 80 calibration
points
in each run. elsewhere
were used to calibrate
The data 16). Where
each particular
spectrum. The (d, p) reaction Q-values used for calibration were derived from the following sources: (i) The neutron binding energies for all nuclei in question from ref. “). (ii) The excitation energies of 13C and 14C from ref. Is), of “N from refs. ‘*,“), of “0 from ref. 19), of 29Si and 3oSi from refs. lv2’), of 31Si, 33S, 35S and 38Cl from ref. ‘), and of 36C1 - the averaged values from refs. 5,9,*o). In deriving the final set of 36C1 excitation energies we included in the analysis fifty-two proton spectra from several runs with different targets containing chlorine as well as CdS targets with chlorine as an impurity.
2.3. DETERMINATION SECTIONS
AND
OF ABSOLUTE TESTING
DIFFERENTIAL
OF OPTICAL-MODEL
CROSS PARAMETERS
Correct evaluation of spectroscopic factors depends on the absolute normalization of the cross section data, on the choice of optical-model parameters, on the boundstate potential well parameters, and on finite-range and non-locality corrections. In table 1 are listed parameters of optical potentials, which are in the given case expected to describe adequately the elastic scattering of particles in entrance and exit channels. In fig. 2 is displayed the angular distribution of u/uR, the ratio of the deuteron elastic scattering cross section to the Rutherford one. The dashed line represents the average
of experimental
data on elastic scattering
of deuterons
by nuclei
in the
mass region from 28 to 40, obtained at deuteron energy of about 12 MeV [refs. 2’*24*25,27,28)]. The dashed area is defined by envelope lines of a/aR curves, calculated with fourteen sets of deuteron optical-model parameters from table 1. The solid curve is the optical-model calculation using parameter set 1 of table 1. In our experiments the chlorine targets of natural abundance were used, i.e. containing 75.77% of 35Cl and 24.23% of 37C1. The target thickness and therefore the absolute cross section was calibrated at &,, = 21” by putting the deuteron elastic scattering cross section u equal to 0.78 ua. Such normalization of absolute cross section is believed to be accurate within about 10%. In fig. 3 are presented the results of DWBA calculations for 1.951 MeV (I = 3), 3.332 MeV (I = I), and 6.085 MeV (I = 1) states with different sets of optical-model parameters, listed in table 1. The calculations have been performed including finite-range and non-locality corrections (FRNL) and also without such corrections (ZRL). The areas in fig. 3 dashed as represented by symbols A and B are defined by envelope lines for the curves of gF&,( 0) and aFRNL nWBA(e), respectively, calculated
3. Piskor'et al. / 36Cl
214
TABLE
Optical b
Set
(MIV)
(Ee$)
w, ‘) (MeV)
potential
1
parameters
(z:V)
rs.0. (fm)
(f?)
Deuterons “)
13 2’) 3 ‘) 4s) 5? 6 ‘) 7j) 8 ‘) 9’) 10 “) 11”) 12”) 13 0) 14’) Protons ‘) I ‘) II “) III ‘)
106.2 107.4 100.6 103.1 102.5 103.0 101.1 109.7 89.9 91.6 112.0 114.6 105.3 56.6
51.4 46.6 50.7
0.188
11.24 9.84 10.20 9.90 9.90 10.50 11.40 10.30 12.33 8.88 18.00 16.20
7.43 7.00 6.00 6.00 6.00 8.00 8.50 8.16 6.97 9.60
0.842 0.860 0.815 0.799 0.813 0.805 0.882 0.809 0.730 0.722 0.900 0.833 0.860 0.928
0.628 0.640 0.666 0.611 0.635 0.580 0.570 0.596 0.744 0.773 0.470 0.548 0.570 0.499
0.583 0.500 0.815 0.799 0.813 0.805 0.600 0.809 0.660 0.722
1.051 1.030 1.070 1.070 1.070 1.070 1.088 1.031 1.170 1.164 1.000 0.995 1.050 1.116
1.553 1.590 1.490 1.530 1.540 1.560 1.562 1.508 1.325 1.374 1.550 1.410 1.510 1.494
0.894 0.750 1.070 1.070 1.070 1.070 0.987 1.031 1.070 1.164
6.20 7.50 8.00
0.750 0.650 0.650
0.549 0.470 0.470
0.750 0.470 0.650
1.170 1.250 1.200
1.320 1.250 1.250
1.010 1.250 1.200
16.70 14.05
1.368
7.81 13.50 11.00
“) All sets have rc. = 1.3 fm. Non-local correction factor p = 0.54. b, W # 0, volume absorption. ‘) W, # 0, surface absorption. d, Parameters derived from those given by Abegg and Datta ‘I), set 1, employing the formulae of ref. 2z), i.e. V, = V,,+0.25(E0-
E,)-2.3(Zo/A;‘3-Z,/A;‘3),
rw, = r,o-0.9(A,“3-A;“3), a,, = a,, -0.082(A;‘3
- A;“)
The subscript 0 refers to the parameters given by Abegg and Datta, whereas the subscript 1 refers to corrected. ‘) 37CI, 12.0 MeV ref. 24). ‘) ?a, 11.8 MeV, ref. 23). those p, 40Ca, 11.8 MeV, ref. 23). “) 38Ar 11.8 MeV ref. 23). ‘)’ Systematics 11.8 MeV, ref. *5). ‘) 39K, 12.8 MeV, ref. 23). k, Ca, 11.8 MdV, ref. 23).‘1) Global potential 26). “) ‘%a, 12.8 MeV, ref. 23). p, 3’P, 12.0 MeV, ref. *3). “) so called “av Z” potential “). “) %a, 12.0 MeV, ref.23). ‘) Ca, 12.1 MeV, ref. 23). ‘) Non-local correction factor p = 0.85. Parameters given for the ground state transition only. ‘) Systematics by Becchetti and Greenlees *9), rc = 1.3 fm. “) Systematics by Perey 30), r, = 1.25 fm. ‘) Modified Perey potential 27), rc = 1.25 fm.
with fourteen sets of deuteron optical-model parameters in the entrance channel (sets 1 to 14 in table 1) and with one set of proton optical-model parameters in the exit channel (set I in table 1). In fig. 3 are also plotted DWBA cross sections calculated with the set 11 of the deuteron optical-model parameters in the entrance channel and with three sets of proton optical-model parameters in the exit channel, i.e. the solid, dashed and dotted curves correspond to cross sections ~~!$aA(‘ti), calculated with sets I, II and III, respectively. In all cases the shapes of angular distributions are very similar. From the analysis of &vBA( O,,,,,) and &i$&( &,,,,),
3. Fiskoi
0.1 I
0
1
I
20
I
et al. I
I
40
275
36Cl
I
1
60
I
I
80 0
Fig. 2. The angular distribution of relative deuteron elastic scattering cross section o/uR. The dashed The optical model calculations with curve is the average of compiled experimental data 21324~25327~28). parameter sets 1 through 14 (table I), all lay within the dashed area. The full-line curve is the opticai model calculation using parameter set 1. Points are our measurements (point at O,, = 21” was used for calibration of absolute cross sections by putting CT/-~ at this angle to 0.78).
calculated with different sets of optical-model parameters, overall conclusions can be made: the sample standard deviations of cross sections in the maxima for the parameter sets of table 1 in the entrance (exit) channels are 8.7% (6..5%), 7.6% (4.4%) and 7.1% (3.8%), while the mean values of a(&,,) suit the approximate relations
for the 1.951 MeV (f = 3), 3.332 MeV (I = 1) and 6.085 MeV (I = 1) states, respectively.
2.4. DWBA
ANALYSIS
A DWBA analysis of angular distributions was performed using the zero-range code DWUCK 31). The bound-state wave function of the transferred neutron was generated using the standard “well depth” routine in which the depth of a singleparticle potential of a fixed Woods-Saxon geometry (r, = 1.25 fm, a, = 0.65 fm) is varied until the single-particle state with given quantum numbers obtains the proper binding energy. The usual factor h = 25 was used in the Thomas spin-orbit term of
20
40
60 80
0
20
40
60
I
I
0
20
il
I
40
Q c. ,“”
I
1
(deg)
j--3/2
I,:
E x= 6084.84
35Cl(d,p)36CI
Fig. 3. Results of DWBA calculations of single-particle cross sections for three %I states, performed with different sets of optical potentials from table 1. The solid, dashed and dotted curves are zero-range and local calculations with set 11 in the entrance channel and sets I, II and III in the exit channel, respectively. DWBA curves calculated with parameter sets 1 through 14 in the entrance channel and set I in the exit channel performed both with finite-range and non-locality corrections and without such corrections all lay within the areas dashed as A and as B, respectively.
0
1.C
1.C
Ex:3332.29
1oc
10I-
-
35CW,p)36CI
IC
lo(
3. Piskor'et al. / 3bCl the same geometry. the calculations. non-locality
The finite-range
The finite-range
correction
factors
and non-locality parameter
for the deuteron
277
corrections
was taken
were included
to be equal
and proton
optical
in
to 0.621. The potentials
were
taken 0.54 and 0.85, respectively. Present DWBA calculations were performed with optical-model potential parameters given in table 1, namely with the set 1 for the entrance channel and with the set I for the exit one. Spectroscopic factors were found by the least-square method of fitting of the theoretical cross sections in the vicinity of the main maxima to the experimental ones, related by
where Ji and Jr are the total angular momenta of the initial and final states, respectively, j represents the total angular momentum transferred by the neutron, SIJ are the spectroscopic factors (fitting parameters), and al,j are the cross sections calculated by DWUCK. Because the target nucleus has non-zero spin, namely J: equals z’, the angular momentum of the transferred neutron is vector-wise added to it, giving the total momentum of the final state. Therefore in some cases two orbital momenta of the transferred neutron, differing in two units, are allowed as well as two different spin orientations for each 1. Because the shapes of angular distributions in single-nucleon transfers are practically dependent on 1 only, experimentally no distinction can be made between transfers with different spin orientations. For this reason only the most probable final single-neutron states are considered, i.e. the 2~,,~, Id,,, and lf,,2 states for 1= I,1 = 2 and I= 3 transfers, respectively, and therefore only the corresponding spectroscopic factors are given. The experimentally observed angular distributions fitted with the DWBA curves are presented in fig. 4. 3. Results and discussion 3.1. ENERGY
LEVELS
OF %I
As should be expected the odd-odd nucleus 36C1 has a very complicated level scheme. Seventy-seven excited states of this nucleus up to 7 MeV excitation energy have been identified in our spectra. In table 2 the excitation energies of the 36C1 levels, found out in the present investigation, are listed together with those from ‘*‘*‘“)] and (p, d) [ref. “)I reactions. (n, Y) [refs. The bulk of today’s most precise data on excitation energies of nuclei or on their neutron binding energies are derived from (n, y) experiments. This is also true for the nucleus 36Cl and as we have used the 35Cl(n, Y)~%ZI data for calibration of our spectra too, let us look at them in more detail. From the thermal neutron capture experiments 5*9,10)extensive sets of spectral components of gamma transitions with high precision quoted are reported, but the data still lack consistency in many points.
3. Piskoi: et al. / ‘6Cl
278
E=788.25 _ 1.0 2 E 2 6 -0
0.1
0
20
40
60
00
0
7
t
E=lb01.41 I=0 j=l/2
20
40
bO
t
E31951.18
I
l=1+3
80
0
20
40
LO
E=1959.16
j=3/2*7/2
1.0
t
0.1
L 80
IQ I
0
20
40
b0
1 80
20
40
60
80
E12467.92
0.1
0
20
40
60
80
0
t
0
20
40
60
I Bern
Fig. 4. Angular distributions of protons from the 35Cl(d , P)~~C~ reaction at E, = 12.3 MeV. The curves are the results of DWBA analysis with finite-range and non-locality corrections included. In cases when the incoherent sum of two I transfers was fitted, both components are also displayed.
279
3. Piskoi et al. / 36CI
r-----E'2863.61
d
xb
I=2
1.0
j.312
-0
1.0
0.1
I
0
IIY.Ih 0 20
.
20
UO
60
10.01
I
40
0
60
20
40
60
1 E=2994.86
:
1
0 1
10.0:
E=3332.29
Es3207.35
t
t
20
40
60
j
:
E=3634.99
: 1.0:
Ea3723.40 I=3
c
0
20
40
60
00
0
20
40
Fig. 4-continued
60
80
0
20
40
60
80
3. Piskoi er al. / %2I
280 7
7
c
10.0:
E=3962.63
0
20
40
60
E=403l.98
1BO
0
20
60
40
0
t
I
40
t
E=4060.53
I=1
1.0:
20
60
I
E'4315.66
I-,
I=1
I=1
1.0
i=3/2
I
2
10.0:
10.0: E=4496.31
0
20
40
60
E=4551.66
80
0
20
40
60
E14598.56
80
0
20
40
60
80
4.m
Fig. 4-continued
:
3. Piskoi et 3
‘=
< 2
E=U753.83
2
1=1+3
0
20
40
60
1
j
t
4
E=4956.47
E=4997.82
I=1
80
F
0
20
40
60
E=5079.18
1=1+3
80 -3
I
t
281
al. / ‘6CI
0
20
E=5204.85
1'1
1.0:
80
80 7 lO.Or------
7
i
0
20
I
20
40
60
i BO
1
0
20
40
Fig. 4-continued
60
40
60
10.0
E=5308.12
0
80
60
10.01
E=5150.40
t
40
E=5463.43
80
0
20
40
60
80 8 cm
3. Piskor’
282
et al. f 36C1
_~-_- .- _ 10.0 E=S619.23
:
4 I." f
0
20
60
80
0
20
UO
60
80
u
a0
0
E"5831.94
t
F
40
.
E=6051.09 1.0 i=UZ+tn
1.0
0.1 0.1
0
20
40
60
I
I
0
20
40
Fig. P-continued
60
I
80
~ 0
20
40
b0
I
3. Piskoi et al. / 36CI
283
T Ee6253.58
0
20
40
60
E36504.60
80
0
20
40
60
80
0
-I 80
20
40
60
20
40
60
7
E=6576.67 I=1 i=3/2
\
0
20
40
60
80
1
0
20
I
40
60
80
0
;
@cm Fig. 4-continued
Spits and Kopecky ‘) reported 420 gamma rays, from which 236 were placed in a 36C1 decay scheme between 72 bound states. Kennett et al. “) assigned 201 gamma rays from the total number of 234 observed ones as being transitions between 64 states of 36C1. By Krusche et al. lo) 236 transitions out of 398 ones, attributed to the reaction 35Cl(n, Y)~?J, were placed in their level scheme of 36C1, consisting of 74 states. In fig. 5 are displayed energy distributions of transitions from the above-mentioned (n, y) experiments. The histograms dashed as represented by symbols A, B and C correspond to data by Krusche et al.lo), by Spits and Kopecky 5, and by Kennett etal.9),respectively. Very surprising in this picture is the low overlap of these three gamma transition sets and also that in these three papers only about 50% of the overlapping transitions are assigned as transitions between the same set of energy levels of 36C1 - see the histogram dashed D type.
s. Piskor’ et al. / 36Cl
284
TABLE Levels
of %I
below
7.0 MeV excitation
and as compiled
2
energy
from previous
as observed in the present measurements
study
E,(keV (4
P) “) 0
(n, Y) “)
(P. d) ‘)
0
J” d,
0
2+
788.444*0.016
789&l
3+
1165.13*0.28
1164.888+0.013
1165*1
1601.41 kO.95
1601.113*0.021
1600*
1951.18kO.49
1951.198*0.020
1959.16*0.29
1959.410*0.013
195851
2+
2467.92 f 0.36
2468.281 *to.028
2467 * 2
3-
2492.33 f 0.45
2492.321*
0.021
2491*2
2+
2518.47k0.14
2518.420+
0.024
2517*2
5-
2675 f 2
1+ (2fS)i
788.25 * 0.48
2676.O;t 1.1 2810.95kO.19
1+ 1
1+ 2-
2676.421 zt 0.041 2810.604*0.038
2863.61 f 0.82
2863.957 * 0.028
2863 * 2
2896.45 * 0.09
2896.342 * 0.026
2894*2
2994.86 f 0.14
2994.691 f 0.034
2995 f 2
(2,3)_ (l-3)_
3099.75 *0.40
3100.724*0.045 3208 * 4
(0-3)_
3207.35 i 0.20 3332.29 f 0.07
4-
3208.62 f 0.29 ‘) 3332.314 f 0.034
3331 i3
3469.1 zt 1.3
3470.036*
3470*
3600.2 f 1.3
3599.549 * 0.036
3634.99 * 0.15
3634.992 * 0.094
0.063
23
(1,2)+
3598 f 3
(1,2)+ 3-
(3661)
(1 -f;+,
3722iz4
4-
3566+4
3663.0+
1.4
3660.494 * 0.190
3723.40 f 0.38 3825.9*
1.7 (1 -4)+
3830.518 *to.425 ‘) 3941.290i0.185 3962.63 * 0.11 3992.06 + 0.08
h,
(l-3)+ 3962 f 4
3962.831 *to.103 3992.40 * 0.21 ‘)
(1 -3)_
4030*
(1,2)_ (O-3)_
3997.553 f 0.294 ‘) 4031.98iO.09
4031.971*0.187
4060.53 f 0.79
4061.473*0.127
4138.8OkO.18
4138.951 kO.118 4205.64OkO.185
4262.0*
1.8
4293.0*
1.8
(2,3)_ h,
4315.60*0.30g) 4410.044*0.216
4496.31*0.12
(1,2)Y 5
h,
4299.700 * 0.211 h) 4315.66+0.17 4405.6 f 1.5
2-
3990 * 4
4205 f 4
(1,2)+
4299 * 3
O+,T=2
4316*4 h,
(O-3)_ (l-3)’
4496.686 * 0.172
2-
4525.235 * 0.145
4524k4
4551.66*0.59
4551.504*0.176
4551*4
4598.56 * 0.09
4598.449*0.173
2+ (1,2)+ 3-
4720 * 4 4724.1 zt 1.5 4738 + 5 4753.83 kO.27
4754.222 * 0.178 ‘)
(2,3)_
3. Piskor'et al. / 36Cl TABLE
285
2-continued
-WkeV) (4 P) “1
(4 Y) “1
(P,4 ‘1
4757.969 f 0.123
J" d, 3-
4823.7 f 1.5 4829.563 +0.148 4843.219kO.294’)
4s30* 5
(1 -4)+
4852 1-4
(2,3)_
4884*4 4953 f 5
(1, a+
4846.7 * 1.5 4876.7 f 1.5 4883.95 f 0.85 4956.47 f 0.33 4997.82*0.16 5079.18 f- 0.50
(O-3)_ 4997.390 f 0.220 5018.115+0.066 5079.169kO.158
(2,3)(1 -4)+ (l-3)_ 5144*6
5150.40*0.47 5204.85 f 0.20
5150.686*0.118 5204.654* 0.123 5246.692 f 0.143
5263.12kO.10 5308.12*0.11
5263.123 zkO.175
(2,3)_ (l-3)’ 5249 f 5
5329.178*0.128 5332.5 f 1.5 (5369.8 * 1.5)“Cl 5463.43 f 0.08
5463.515*0.125 5473.709*0.161
(2,3)_ (l-3)_
(2,3)_ (1,2)_ (l-3)_ (o-3)+
(1,2)_ (o-3)+
h,
5512.8* 1.5 5517.747*0.107
5517*5
3-
5545.0* 1.5 5578.31 f 0.22
5563.633 +0.130 5578.500*0.115 5604.467 f 0.134
5605 * 5
5619.23 + 0.09 5694.42 * 0.21 5703.152iO.138 5734.116*0.129 5778.304i 0.232
5702 l 5 5734*6
5831.94*0.38 5866.6* 1.5 5898.48 kO.10 5912.01*0.11
(2-, 3) 22+ (O-3)_ (O-3)_ (2,3)_ (2,3)_ (l+-3) (O-3)_ (O-3)_ (O-3)_
5913*5
(1,2)+
5957*5
(1,2)+
5986 f 5
(2,3)_ (2,3)+ (O-3)_
5947.6 + 1.5 5956.762 f 0.142 5967.6 f 1.5
6051.09*0.31 6084.84 * 0.08 6089.883 f 0.207 g)
(2,3)_ (l-3)
s. fiskor’ et al. / 36CI
286
TABLE 2-continued
ESkeV) (4 Y) 9
(4 P) “)
6184.95510.151 6236.41 f 0.53 6253.58rtO.13 6268.34 * 0.75 6340.35 f 0.26
(P, d) ‘) 6095 f 5 6146*5 6184*5
r)
6253.734*0.180’) 6268.398* 0.152 6340.020 f 0.254 ‘) 6344.350+0.163 6354.930 * 0.190 ‘) 6379.547 kO.131 6423.483 f 0.152
6354*6 6379 f 5 6423 f 5 6480 f 7
6487.739ztO.159 6504.60 f 0.47 6528.43 * 0.50 6538.210*0.213
h,
J”“) (1,2)’ (1,2)’ (1,2)’ (2,3) 2(2X-4’) (l-3)_ (1.2)’ (1.2)’ (1,2)’ (2.3) (2,3)(l-3) (2,3)Y (l-3)
6539.8 * 1.5 6545.032ztO.138 6550* 5 6576.67 * 0.50 6595.18 f 0.78 6604.57 * 0.64
6596 f 7 6604.380*0.213
h, 661855
6642.752kO.157 6673.13 kO.15
6773.207 f 0.185 h,
(l-3) (I, 2)+ (O-3)_ (2,3)Y (l-3) (O-4)’ l_
6683 i 5 6750*6 6774 f 6 6826*6
(2,3)Y (2,3)Y (1,2)+ (o-4)+ (o-4)+
6893 f 7
(l-3) (1,2)+
6836.521 kO.203 “) 6950.02 * 0.7 1 6952.404 f 0.241
(I-3) (O-3)_
6997.14kO.21
“) Present work. States with quoted errors exceeding one keV are weakly populated in the (d, p) reaction and their assignment to %Zl nucleus is probable but not certain. ‘) The weighted average of three (n, y) measurements sS9,‘a). The quoted errors are those of weighted means multiplied by the overall consistency factor 2.64 for the whole set of (n, y) states or by the local consistency factor for each particular state, whichever is greater. The consistency factors 34) are defined as follows F,=(l/(n,-1)
:
((E;-E;,)2/u;))“*
the local consistency
factor,
j=1
F=(l/(N-M)
c” 2 ((E,-E,)*/a2,))“’ I=1 j-1
the overall
consistency
factor
3. Piskor'et al. / 36CI
287
TABLE 2-continued where index j denotes different measurements (n-number of authors) and index i denotes different states (M-total number of states, N =C,“_, n, total number of measurements). Twelve of the states reported by Spits and Kopecky ‘), not confirmed by Kennett et al. ‘) and by Krusche et al. lo), are not included in the table. For reliability and consistency of (n, y) data see text. ‘) From ref. 4). d, Spin-parity assignments from ref. I), from the present work and from the application of recommended upper limits 32) to the y-ray strengths computed from the y-ray branchings 5.9,‘o) and lifetimes I). “) ‘) s) Not ‘) ‘)
Reported in refs. 5.9), but not in ref. lo). Reported in refs. 9,‘o), but not in ref. 5). Reported in refs. ‘,t’), but based on different reported in ref. ‘). Reported in ref. lo) only. Reported in ref. 9, only.
2000
4000
transitions.
6000
8000
E, keV
Fig. 5. Histograms representing the energy distributions of measured gamma transitions from three different (n, y) experiments. The histograms dashed as A, B and C are results of papers by Krusche et al. lo), by Spits and Kopecky 5, and by Kennett et al. 9), respectively. The histogram dashed as D represents the number of transitions to which in all three papers the same interpretation was given.
3. Piskoi et al. 1 36Cl
288
In deriving which
errors
are presented
overall consistency
of averaged
excitation
energies
from the (n, y) experiments,
column
of table
2, for 54 common
in the second
factor 2.64 was necessary.
states were much greater,
The local consistency
states the
factors for some
e.g. for the 3100.724 keV state it amounted
to 6.45 (see
table 2, note b). Applying the consistency factors to the final errors, we cannot, unfortunately, take into account the systematic uncertainties, i.e. that the resulting excitation energies of some states are biased due to the fact that though they are based on the same gamma transition sets in all three works, it is possible that some of the transitions are wrongly assigned. Fortunately on the other hand there exists a sufficient number of strongly populated states to which the accurate and precise gamma transitions are probably correctly assigned, though some small components hidden in strong lines can hardly be distinguished. In any case, the excitation energies based on the Ritz combinational principle only must be taken with caution and more careful analysis of the existing (n, 7) data as well as coincidence measurements seem quite desirable. Most of our new or readjusted energy levels of 36C1 nucleus in the first column of table 2 are believed to be reliable within quoted errors. The reason for this is that we used as many as possible independent calibration data (up to 80 calibration points in about 8 MeV energy interval) in which 36C1 data amounted to 30-40%. Some weakly populated states given in the first column with quoted errors exceeding 1.0 keV are probable but not with certainty established states of 36C1. They were observed with low statistics at few reaction angles only. The set of excitation energies from (p, d) reaction in Rice et al. “) are found to be quite accurate with pessimistic estimates of precision given. This is not the case with (d, p) energies in Hoogenboom et al. ‘) (not presented in table 2) where precision of about 8 keV was quoted and for which differences of more than 10 keV were found. The angular momenta and parities of 36C1 states presented in the last column of table 2 are based on the review article by Endt and Van der Leun ‘) including assignments from the (p, d) reaction 4), on our Z-assignments from the (d, p) reaction and on the application of the recommended upper limits for strengths transitions of given multipolarity 32) to the (n, y) measurements. 3.2. SPECTROSCOPIC
FACTORS,
I- AND
of gamma
r-ASSIGNMENTS
The experimental angular distributions agree quite satisfactorily with the DWBA calculations. In most cases this enabled us to assign unambiguously the transferred orbital angular momenta I to the main components of angular distributions and consequently to derive parities of states in question and to extract the corresponding spectroscopic factors. We have fitted two Z-components in the cases where their presence was evident. Nevertheless, most of the angular distributions, classified in fig. 4 as being pure I = 1 transitions, reveal a typical feature, i.e. that outside the
3. Piskor'et al. / ‘6CI main maxima
the experimental
cross sections
clear if this is due to the possible neutron
transfer,
uncertainties
presence
or if it is an indication
of optical-model
parameters.
289
exceed the theoretical of a small
I= 3 component
of DWBA The point
ones. It is not
limitations
in a given
including
the
is that such a behaviour
I = 1 angular distributions was observed also in some (d, p) experiments in energy and mass region, performed on even-even targets, i.e. where only I-component is allowed, see e.g. 34S(d, p)3sS in Abegg and Datta 2’). So when are quoting the pure Z= 1 component, in some cases the presence of small
of this one we 1= 3
component is possible. Our I-assignments and spectroscopic strengths for states below 3.4 MeV are given in table 3 in comparison with those of Decowski 3, and with theoretical values of spectroscopic strengths calculated in the full space of sd-shell-model wave functions for positive-parity states by Wildenthal et al. “). With the exception of the ground state and 2863.61 keV state transitions the consistency of our data with those by Decowski is quite satisfactory. We can compare neutron stripping spectroscopic strengths given in table 3 with the proton stripping strengths for transitions to the first two analog states in 36Ar (i.e. J” = 2+, T = 1 and J” = 3+, T = 1) observed in the reaction 35C1(3He, d)36Ar by Moinester and Parker Alford 33). Though both neutron stripping values for the transition to the first excited state in 36C1 are in good agreement with the value 2.18, observed in ( 3He, d) reaction, spectroscopic strengths for the transition to the ground state observed in (d, p) experiments exceed significantly the value 3.84 given by Moinester and Parker Alford. From comparison in table 3 of observed (d, p) spectroscopic strengths with those calculated by Wildenthal et al. “) we see that the experimental values exceed considerably the theoretical ones. It should not be surprising as one can expect that due to pairing effects the single-particle orbits with higher orbital momenta, namely the lf7,* orbit for instance, are partly populated in the ground state of 35C1 and therefore sd-orbits are emptier than is expected in the simple sd-shell-model or in the above mentioned as active. The configuration take into account
calculations, space neither
where only Id,,,,
used in the calculations the negative-parity
2s,,* and Id,,, orbits are treated by Wildenthal
states of %l,
et al. allows to
nor some real positive-
parity states, the so-called intruder states, the true eigenfunctions of which are a mixture of pure sd-shell states and even-parity fp-shell distributions. Hasper I*) performed shell-model calculations in augmented configuration space, where also particles in lf,,* and 2p,,, shells were treated as active, though the Id,,, subshell was not included in the model used in his study. Unfortunately from our point of view the 35CI was not calculated by Hasper, i.e. the 35C1 ground-state wave function calculated in the frame of used configuration space is not available. This does not allow us to calculate spectroscopic factors, especially for negative-parity states, and compare them with the experimental ones. Nevertheless, a qualitative comparison is possible.
3. Piskor'et al. / 36Cl
290
TABLE
Values of 1 and (25,+ l)S, for the reaction
(da/do);:
I
3 35Cl(d, P)~‘CI (states below 3.4 MeV)
Experiment
Theory b,
(mb/sr) This work “) 0
788.25 1165.13 1601.41 1951.18 1959.16 2467.92 2492.33 2518.47 2810.95 2863.61 2896.45 2994.86 3099.75 3207.35 3332.29
1.62 0.61 2.64 1.75 1.25 3.28 3.44 1.12 2.66 1.10 0.41 5.50 3.37 0.41 2.07 7.34
032 2 032 0 1,3 0 1,3 092 3 3 2 1,3 1 3 1 1
0.19,5.89 2.23 0.34,0.94 0.22 0.30,3.99 0.39 0.90,4.58 0.12,0.30 10.17 4.08 0.95 1.45,2.05 0.90 1.46 0.53 1.86
Ref. ‘) < 0.07, 8.21 2.03 0.33, 1.03 0.14 -, 4.26 0.53 0.76, 5.37 0.15, 9.32 4.11 4.16 ‘) 1.45, -
2s I/2
Id,/,
ld,,,
0.03 0.19 0.03
3.59 1.33 0.44 0.09
0.01 0.11 0.03 0.02
0.15
0.03
0.13
0.25
0.00
0.15
0.00
0.42
? *) 0.50 1.79
“) Values for I= 0, 1,2,3 are for 2s,,,, 2p,,,, Id,,, and If,,, calculations, respectively. Spectroscopic factors Sj for 2p,,a, Id,,, and lf5,a transitions can be related to those presented by means of the following approximate relations: S,,,,a = (1.15 -0.04 E +0.003 E’)S,,,,,, S,,,,, = S,,,,,/(1.21+0.031 E) E+o.oll E2)S,,,,,, where E is the excitation energy in MeV. and S3.5,2 =(1.54-0.105 b, Average values of calculations made with four different effective hamiltonians in the full space of sd-shell-model wave functions for positive-parity states 6). ‘) Values for 1~3. d, Not measured.
Let us look, e.g., at the state 2863.61 keV. Contrary to Decowski ‘) (as well as to Hoogenboom et al. ‘) we have found the positive parity for this state in accordance with the result of the (p, d) experiment. From (n, y) measurements the possible spin of this state is 2 or 3. Calculations by Wildenthal et al. “) give only three 2+ states in the range up to 4 MeV. Therefore in the frame of their model the state 2863.61 keV could be the second 3+ state originating mainly from the orbit Id,,, (see table 3). In the energy range up to 4 MeV the calculations by Hasper ‘*) give two more 2+ states in comparison with the sd calculations. The possible candidate for the state in question could be the fourth 2+ state at 3.05 MeV with the following main components of wave functions: 53% s-‘dM3 and 17% sP’dP5f2. From a qualitative point of view a relatively strong 1= 0 component should be expected in populating such a state. As is seen from table 3, this state has the pure I = 2 component only. Therefore the 2863.61 keV state should be more probably interpreted as a second 3+ state.
3. Piskoi et al. / 36CI Orbital
angular
momenta
1 and the corresponding
states above 3.4 MeV are presented Orbital
angular
spectroscopic
strengths
for
in table 4.
1 assigned
momenta
291
in PWBA analysis
et al. ‘)
by Hoogenboom
agree in most cases quite satisfactorily with ours. We can check, at least qualitatively, the set of derived spectroscopic factors by applying the sum rules, i.e. that the sum of weighted spectroscopic factors should be equal to the number of neutron holes in the target nucleus in a subshell n, 1,j (or in a subshell n, I- when we do not distinguish between different spin orientations, i.e. between j = 1 +a and j = 1-G orbits). The weights are the well-known statistical factors (2Jr+ 1)/(2Ji + 1) and the summation has to be extended over all the final states (whatever the Jr) which can be reached by transfer of a neutron in the subshell n, 1,j (or in the subshell n, 1). Sums of weighted spectroscopic factors from our experiment are in table 5 compared with those of Decowski 3), with the theoretical ones of Wildenthal et al. “) and with the simple shell-model estimates. According to the note “) below table 3 a slightly smaller value is expected for I= 2, whereas somewhat greater values could appear for I= 1 and I= 3. Values for I= 1 and I= 3 could also be uncertain to some degree due to the already discussed problems, i.e. that some angular distributions considered in our analysis as having a single-l character could be in fact superpositions of two l-components.
TABLE Values of I and (25,+
1)s for the reaction
35CI(d , ~)~%l
4 (states above 3.4 MeV) as observed
in the present
investigation
(du/dfi);:
I
(2J,+l)s,“)
(du/dfl)F: (&
,
(mb/sr)
(25,+
I)%“)
3600.2
0.33
1
0.08
5263.12
3.01
1
0.56
3634.99
1.77
1
0.43
5308.12
2.94
1
0.55
3723.40
0.35
3
1.12
5463.43
4.34
1
0.78
3962.63
2.40
1
0.55
5578.31
0.81
0.11,0.75
3992.06
4.15
1
0.94
5619.23
3.77
1,3 1
403 1.98
3.43
1
0.78
5694.42
0.98
1
0.17
4060.53
0.41
1
0.09
5831.94
0.67
1
0.11
4138.80
1.53
1
0.34
5898.48
3.22
1
0.53
4315.66
1.67
1
0.37
5912.01
2.50
1
0.41
4496.31
4.17
1
0.89
6051.09
0.98
1
4551.66
0.50
0,2 1
0.03,0.33
6084.84
5.97
L3
0.91,0.82
6236.41
0.10,0.67
0.15,0.44
193 1
0.27,0.45
0.25
6253.58 6340.35
0.88 1.92
133
1,3 1
0.24, 1.10
6504.60
2.71
193 1
0.38,0.24
193 1
0.21, 0.38
0.70
4598.56
3.33
4753.83
0.79
4956.47
1.29
4997.82
1.41
5079.18
0.57
1,3 1
0.11
6576.67
1.02
5150.40
0.72
1
0.14
6673.13
1.66
5204.85
2.80
1
0.53
6997.14
1.53
“) See comment
“) below
1.16
table 3.
b, For I = 0, 2 the values of (25,+
l)S, are equal to 0.01 and 0.69, respectively.
0.66
0.16
0.17 0.14 0.20
b)
3. Piskoi et al. / j6CI
292
TABLE
Comparison
of experimental
and theoretical
5
sum rules for neutron 2p orbitals
stripping
into 2s, Id, If and
1 [w,+1)/wi+1)1~, Jr(U I
Experiment Present
Theory
Decowski
a)
Wildenthal
0.31 2.82 b,
0.32 2.66 8.08 4.74
er al. “)
Simple shell-model
0.18 1.61
If and 2p empty, “) 2s filled; Id,,, half-filled; b, Not included states 2863.61 keV (different
i.e. number
I assigned)
“)
0 2.0 14.0 6.0
of holes = 2 (21+ 1). and 4551.66 keV (not measured).
From table 5 we see that the significant parts of If and 2p single-particle are exhausted by states up to 7 MeV observed in our experiment.
strengths
4. Conclusions Excitation energies of 77 states up to 7 MeV were obtained through the 35Cl(d, ~)~%l reaction. Eighteen states; 3207.35, 3723.40, 3992.06, 5308.12, 5619.23, 5694.42, 5831.94, 5898.48, 5912.01, 6051.09, 6084.84, 6236.41, 6504.60, 6528.43, 6576.67, 6596.18, 6673.13 and 6997.14 keV, are new or established with almost two orders higher precision than was quoted in the earlier (d, p) experiments. Eight states: 4031.98,4315.66,4496.31,4598.56,4997.82,5263.12, 5463.43 and 6253.58 keV, were established
with higher
precision
than in the (n, y) experiments.
Precision
of
about 70-80 eV achieved for some strongly populated states is quite unusual in experiments with charged particles. DWBA analysis of angular distributions allowed us to deduce 1 and absolute values of spectroscopic factors for 51 states. Based on I-assignments the spin and parity restrictions were obtained l-assignments are in agreement. for the first time.
for these states. Where J” values are known, our Spectroscopic factors for 36 states were obtained
References 1) 2) 3) 4) 5) 6)
P.M. Endt and C. van der Leun, Nucl. Phys. A310 (1978) 1 A.M. Hoogenboom, E. Kashy and W.W. Buechner, Phys. Rev. 128 (1962) 305 P. Decowski, Nucl. Phys. Al69 (1971) 513; Al96 (1972) 632 (erratum) J.A. Rice, B.H. Wildenthal and B.M. Preedom, Nucl. Phys. A239 (1975) 189 A.M.J. Spits and J. Kopecky, Nucl. Phys. A264 (1976) 63 B.H. Wildenthal, EC. Halbert, J.B. McGrory and T.T.S. Kuo, Phys. Rev. C4 (1971) 1266
3. Piskofet al. / 36CI 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28)
29) 30) 31)
32) 33) 34)
293
C.M. Bhat, N.G. Puttaswamy and J.L. Yntema, J. of Phys. G7 (1981) 1529 M.L. Stelts and R.E. Chrien, Nucl. Instr. Meth. 155 (1978) 253 T.J. Kennett, M.A. Islam and W.V. Prestwich, Can. J. Phys. 59 (1981) 93 B. Krusche, K.P. Lieb, H. Daniel, T. von Egidy, G. Barreau, H.G. Borner, R. Brissot, C. Hofmeyr and R. Rascher, Nucl. Phys. A386 (1982) 245 E.G.Jr. Kessler, G.L. Greene, R.D. Deslates and H.G. Biierner, Phys. Rev. C32 (1985) 374 H. Hasper, Phys. Rev. Cl9 (1979) 1482 P. Franc, J. KIemCnek, S. Piskoi and W. Schaferlingova, Czech. J. Phys. B29 (1979) 1084 R. Batter, J. Kiemtnek, S. Piskoi, Z. Svoboda and V. Skaba, Nucl. Instr. Meth. 157 (1978) 83 V. Kroha and K. Putz, 7th Conf. of Czechoslovak Physicists (Czech. Union of Math. and Phys., Prague, 1981) p. 02-36 P. Franc, J. Kiemenek, S. Piskoi and W. Schaferlingova, Nucl. Instr. Meth. 211 (1983) 159 A. H. Wapstra and G. Audi, Nucl Phys. A432 (1985) 1 F. Ajzenberg-Selove, Nucl. Phys. A360 (1981) 1 F. Ajzenberg-Selove, Nucl. Phys. A375 (1982) 1 T.J. Kennett, W.V. Prestwich, R.J. Tervo and J.S. Tsai, Nucl. Instr. Meth. 215 (1983) 159 R. Abegg and S.K. Datta, Nucl. Phys. A287 (1977) 94 J.A.R. Griffith, M. Irshad, 0. Karban and S. Roman, Nucl. Phys. Al46 (1970) 193 C.M. Perey and F.G. Perey, At. Data Nucl. Data Tables 17 (1976) 1 G.P.A. Berg and P.A. Quin, Nucl. Phys. A274 (1976) 141 W. Fitz, J. Heger, R. Santo and S. Wenneis, Nucl. Phys. Al43 (1970) 113 W.W. Daehnick, J.D. Childs and Z. Vrcelj, Phys. Rev. C21 (1980) 2253 R.H. Bassel, R.M. Drisko, G.R. Satchler, L.L. Lee, Jr., J.P. Schiffer and B. Zeidman, Phys. Rev. 136 (1964) 960 A.N. Vereshchagin, I.N. Korostova, O.F. Nemets, L.S. Sokolov, V.V. Tokarevskii, I.P. Chernov and A.A. Yatis, Elastic scattering of 13.6 MeV deuterons, Institute of Physics of the Ukrainian SSR Academy of Sciences, Kiev (1970) F.D. Becchetti, Jr, and G.W. Greenlees, Phys. Rev. 182 (1969) 1190 F.G. Perey, Phys. Rev. 131 (1963) 745 P.D. Kunz, Instruction for the use of DWUCK: a distorted wave Born approximation program, Univ. Colorado report COO-535-606; Algebra used by DWUCK with applications to the normalization of typical reactions, Univ. Colorado report COO-535-613 (1970) P.M. Endt, At. Data Nucl. Data Tables 23 (1979) 3 M.A. Moinester and W. Parker Alford, Nucl. Phys. Al45 (1970) 143 A.H. Wapstra and N. B. Gove, Nucl. Data Tables 9 (1971)