The 36Ar(d, α)34Cl reaction at 19 MeV

1

2.F

1

Nuclear Physics A180 (1972) 37-48; Not to

@ North-Holland Publishing Co., Amsterdam

be reproduced by photoprint or microfilmJwithout written permission from the publisher

THE 36Ar(d, a)34C1 REACTION AT 19 MeV R. N. HOROSHKO and M. H. SHAPIRO t Nuclear Structure Research Laboratory tt, University of Rochester, Rochester, New York Received 21 September

1971

Abstract: The 36Ar(d, a)34C1 reaction was used to study level properties of %l up to 3.6 MeV excitation. The observed angular distributions are found to exhibit a systematic L-dependent structure which confirms the spin and parity assignments for most of the known 1+ states and places J” limits for some other states. The DWBA analysis was performed using the s+-d+ shellmodel wave functions of Glaudemans. The calculated relative cross sections are in satisfactory agreement with measurements for only a few low-lying states. Considerable configuration mixing in 34C1 is indicated.

E

NUCLEAR REACTIONS 36Ar(d, a), E = 19 MeV; measured E,, relative o(E,, 0,). 34C1 deduced levels, J, x, Ld. DWBA calculations: d+-sf- shell-model wave functions.

1. Introduction The usefulness of the direct (d, a) reactions in nuclear spectroscopy has become apparent 1- “) in recent years principally due to the strong L-dependent structure often exhibited by angular distributions, and also because of a rather restrictive selection rule AJ = L+ 1, which limits the spin and parity assignments more narrowly than is customarily possible from a single-nucleon transfer reaction measurement. While absolute (d, a) cross sections cannot at present be reasonably predicted, interpretation of the relative cross sections provides a valuable test of the nuclear model wave functions. Furthermore, the AT = 0 selection rule is useful in identifying the isospin, particularly in nuclei such as 34C1 where both T = 0 and T = 1 states occur at low excitation energies. The level scheme and level properties of many states in 34C1 have been previously established from the 33S(3He, d) and 35Cl(p, d) reactions 4-6). Spins and more precise excitation energies of several levels have been determined via the 32S(3He, py) angular correlation 7-9) and the 33S(p, 7) measurements lo). The isospin of the lowlying levels has been studied with the (d, IX)and (p, 3He) reactions 11) at 45 MeV although no DWBA fits to the (d, a) data were attempted. Shell-model calculations have been published by Glaudemans 12) for the evenparity states within the d+-s, shell-model space, and by Ernk 13) for the negativet Present address: California State College, Fullerton. t+ Work supported by the National Science Foundation. 37

R. N. HOROSHKO

38

AND M. H. SHAPIRO

parity states by considering the dt-fS orbits. Glaudemans’ calculation gives essentially the correct spins for the first few excited states although in the calculation the 0:

and the 3:

states are inverted

and nearly

states are separated too much. The present investigation was undertaken

degenerate,

to determine

while the lowest two 1’ the level properties

of 3’C1

up to 3.6 MeV excitation via a DWBA analysis of the (d, m) data, and to test the available shell-model wave functions by comparing the calculated and measured relative (d, a) cross sections. 2. Experimental

procedure

The 36Ar target gas (99.6 % enriched) used in this experiment was contained in a rotating gas target cell similar in design to that reported by Zurmiihle and Fou I’). The cell is 5.08 cm in diameter, the cell window subtends an angle of 310” and the cell body is driven through an angle of approximately 100” by a pneumatic windshieldwiper motor connected to the cell by a commercial rotating vacuum seal. The motor provides a constant angular speed and a rapid reversal of motion at the extreme positions of the cell. A 6.35 x 10e3 mm Kapton + film used for the cell window proved to be quite resistant to both heat and radiation damage. The 19 MeV deuteron beam used to bombard the cell was tightly collimated (2 x 2 mm) and was moderately intense (l-2 /‘A). Under these conditions and using i atm pressure in the gas cell, the Kapton films normally survived in excess of 50000 PC bombardments. A collimator assembly fabricated from tantalum stock with three interchangeable circular apertures was used with the cell to define an effective target length of 0.48 cm (at 90”) inside the cell. The collimator system ensured that no scattered particles from the window of the cell would be detected even at the most forward angles used. The geometrical G-factor 1“) for the cell and the collimator assembly was calculated by numerical integration for the angular range used. Negligible deviation from a simple (I/sin 0) dependence was found. A detailed view of the gas cell and collimator geometry is shown in fig. 1. The outgoing cr-particles were momentum analysed with the Enge split-pole spectrograph, and were detected in 100 pm Ilford KO nuclear-emulsion plates. Points on the angular distribution were obtained every 5” in the lab frame from 15” to 75” and at 85” and 95”. The resolution width for individual a-particle groups was about 75 keV. The major contribution to this width was the straggling of the outgoing rparticles in the gas and the Kapton exit window. As a result, the resolution did not change appreciably even at the forward angles. In spite of the 75 keV resolution plates were chosen for detection purposes over solid-state counters placed in the scattering chamber to avoid problems from the intense neutron background caused by the beam striking the Faraday cup. Normalization for the angular distributions was obtained 7 E. I. DuPont de Nemours and Co., Film Department,

Circlevill, Ohio.

39

36Ar(d, a)34C1 REACTION

from the beam integrator and the elastic deuteron group observed with a thin NaI counter mounted at 45” to the incident beam. The (d, cx) spectrum obtained at 30” is shown in fig. 2.

spectrograph

Fig. I. Spectrograph

scattering chamber showing entrance slits, gas cell, Faraday collimator assembly at the entrance to the spectrograph.

%Ar(d ,a)34CI

E, = 18.7MeV eL = 300

cup and the

e, =85” 3.334

3.:34 i .3.377

l

/I{ I I i

2 z200

j

3

\

i \

I I ,x_ 8222226

8

64 100

0

DISTANCE

ALONG PLATE (mm3

Fig. 2. A complete 36Ar(d, ~r)~~Cl a-particle spectrum observed at 13~= 30” and a portion of the 6‘ = 85” spectrum showing excitation of the 3.38 MeV T = 1 state. The deuteron energy shown is the effective energy at the center of the gas cell.

40

R. N. HOROSHKO

AND

M. H. SHAPIRO

The raw excitation energies obtained from the (d, a) spectra with a spectrum peeling and calibration program used on the Rochester on-line computer system were corrected by an amount determined by assuming that the excitation energy of the lowest observed a-group to be 146.8 Ifr1.0 keV as measured by Graber and Harris lo). The ground state is not expected to be seen since it has J” = O+, T = 1 such that its excitation in the 36Ar(d, &) reaction is forbidden by both the isospin and the parity selection rules “). The raw excitation energies of the lowest group observed at various angles differed by up to 8 keV from the value of ref. lo) noted above. The overall energy calibration over the full range of measurements (up to 3.6 MeV) is believed accurate to within 20 keV. 3. The DWBA analysis The DWBA calculations for the 36Ar(d, CX) reaction were performed with the code DWUCK 1‘) using the two-nucleon structure factors compiled by Glendenning “). Finite-range corrections and non-local potentials were included in accordance with suggestions by Daehnick et al. ‘). The form of the potential and the parameters used are summarized in table 1. For the entrance channel, the deuteron parameters were taken from Perey and Perey r9). No spin-orbit interaction was used since this interaction is expected to modify the calculated (d, cc)angular distributions only slightly “). For the exit channel five sets of a-particle potentials are given by McFadden and Satchler *’ ), all of which yield equally good fits to the elastic scattering data. We find that the (d, a) data is more restrictive and only two parameter sets (V, = 142 and 195 MeV) give good overall fits to the observed angular distributions. Fits with both of these parameter sets are shown in fig. 3 for those cases where angular distributions appear to be dominated by a single L-transfer. On the basis of these fits it is difficult to pick one best parameter set and the choice of V. = 195 MeV for the remainder of the DWBA analysis was made because there is some indication from previous studies “) that the deeper potential well may be preferred. We note in agreement with Daehnick et al. “) that the calculated angular distributions show a simple and systematic L-dependent structure which hardly changes with Q value or the details of the deuteron pick-up, i.e. the shell-model assignment of the transferred particles. In the present calculations all possible combinations of the d,, d,, s3 and fS assignments were tried for the transferred pair, and for any given L-value the calculated angular distributions are essentially identical in all cases. In a (d, LX)reaction on a spin-zero target, transitions are generally expected to occur with a mixture of L-values differing by two units. The spin of the final state is given by J = L, Lf 1, and a recognition of two contributing L-values determines the J” uniquely. In cases where J = L, no L-mixing is possible. In order to compare the data with the DWBA calculations where apparently two L-values contribute, a least-squares determination of the experimental cross sections attributable to each L-value was made in a manner analogous to the x2 versus 6 anal-

1

d-Ar a-Cl

Y

:;

ref.

142.0

98.5 195.0

(ML)

“) Ref. tg).

“) Ref. 20).

1.261

1.070 1.210

(Z)

1.5

1.070 1.5

(zl)

0

0 0

parameters

x’ = (r-ro’A+)/a’.

0

20.27 0

-& (1 +ex’)- 1,

16.2

0 19.2

(izk)

0.740

0.483 0.721

(&)

Imaginary well parameters

1.261

1.570 1.210

C*d, Non-local and finite-range parameters,

respectively 2).

light particle and a uniformly charged sphere of radius Rc = rcA+.

x = (r-roA+)/a,

u(r) = U&r)- V(1 Sex)-’ -_iW(l +ex’)-+4jWD

0.740

0.931 0.721

0%

UC is a Coulomb potential between a point-charge

2

set

channel

Real well parameters

Optical-model

TABLE1

0.20

0.54 0.20

0.40

0.40 0.40

R?

$ $

K ;

B ?I%.

42

R. N. HOROSHKO

AND M. H. SHAPIRO

442 3.34 MeV L=3

0

20

40

60

80

100

--r/

’

0

20

40

60

80

100

8c.m.

Fig. 3. The DWBA fits to the (d, or) angular distributions The solid and dashed curves are calculated with parameter

dominated by single L-transfer values. sets 1 and 2, respectively (see table I).

ysis of the y-ray angular correlation data. Fig. 4 shows the x2 versus L+L’ curves for all states studied. The solid curves represent x2 values for even L and the dashed curves for odd L. The number of points used in the least-squares fitting procedure (7 to 10) was obtained from fig. 3 by inspection and corresponds to the angular ranges over which the pure L-fits appear reasonable. In identifying the L-transfer values and L-mixing from the x2 versus L+L’ carves, no fixed procedure such as the 0.1 % probability cut-off was used. The quality of the fits depends on the accuracy of the DWBA calculations as much as on the experimental data and may be L-dependent. For example, for the 3.15 MeV level the x2 values are large because the DWBA fails to reproduce accurately the very strongly structured and accurately measured experimental data (see figs. 3-5) characteristic of a dominant L = 0 transition. Yet for this state, in spite of the large x2 values, the fits with L = 1, 2, 3,4 and 5 and with mixtures of these vaiues are clearly inferior to the fit obtained with an L = 0 + 2 mixture; the latter fit is more probable than any of

0.147

\I

LOX

t

I

\

‘._A,

2.38

-

-

i

,

I

‘I-

-

:’c

ox

0.46

2.59

:

’

I

’II

:

/

2.73

IF

I

-L-even ---L-odd

Fig. 4. The x2 versus L+L’ curves for the states studied. The solid and the dashed curves represent L-even and L-odd mixing, respectively. The three horizontal lines drawn for each state represent probability values of 0.02, 0.01 and 0.001 with respect to the minimum point on the curve.

4

4

IO /

40

I

Fig. 5. Angular distributions and the DWBA fits for all levels studied. The curves represent fits using the L-values and L-mixtures determined from the x2 analysis illustrated in fig. 4. The level at 3.64 MeV is an unresolved multiplet.

8c.m.

p w

2-(o-,

1(81&20)+3 0(60&21)+2 3(100&40)

“) p, q, ‘) “)

“) ‘) k, “)

3+(4+, 5+) “) 1+ 1+

2+4(87&20) 0+2(73413) 0(61 f12)+2

2-, 3!:42+,T=

(1 z)+ 2“) 1

2+ 2+ 3+ 4+ 5+ ‘) 2;,T’= 1 3+ 4+ and 1+ k,

3+ 1+ 1+

0+, T = I

Jn, T

Combined

Ref. 23). b, Ref. IS). “) Ref. ‘). d, Ref. s). ‘) Ref. I”). ‘) Ref. II). Assuming positive parity. Possibly a doublet, the level observed in the (d, a) reaction is definitely not Jn = 4+. Negative-parity assignment is favored by a factor of over 100 on the basis of x2 values. In ‘) the Z-transfer value for this level is listed as doubtful. DWBA calculations using s&-d3 shell-model wave functions of Glaudemans et ul. I*). Not observed. The Jn values in parentheses are less probable but allowed within the errors in L-mixing. Calculations for the 13+ state. Errors w 20 keV.

;;.I:,+ g) 2+ C*f), T = 1 ‘)

1-) “) 1+ 2-, 3-, 4-

3+ , 4+ , 5+ ‘)

2191 2382 2589 2620 2125 3146 3334 3377

;I+:;)+ ‘) 2+ b*‘), T = 1 b.‘) 1+,2,3+ b*c) 4+ b,c 1 csq,)1+ ‘) (I-3)f ‘) 2 d,C), 2- ‘)

1229 1890

2 “), 2+ ‘)

1228.8hO.7 “) 1885.9&1.6 ‘) 1923.3f1.7 *) 2158.4-fl.2 ‘) 2179.4&1.4 b, 2375.6kO.7 “) 2580.6f1.3 ‘) 2608 &2 g, 2720.4+1.6 ‘) 3128 &Zp) 3333 32 ‘) 3383 *2 ‘)

3+, 4+, 5+ 1+ 1+ 3+ 1+, 2+, 3+

Jr limits

4(100&18) 0+2(61&11) 0+2(66&17) 2 +4(44&20) 0+2(91 f41) 2+4(57&22) 3+5(52f22)

= 1 “)

Experimental

L( % mixing)

a)

147 459 665

o+,T

E(keV) “)

(d,

3+ “) ,+ b.C) I+ c-l )

0

Previous Jn and T assignments

146.8*1.0 ‘) 461.5*0.3 “) 664.610.3 ‘)

E (keV)

TABLE2 The present results

‘) Ref. 5).

9 6.3 0.9 22.1 $ 4.4 5.9 16.8 38.8 <4

4.0 3.3

< 0.05 9.6 26.0 4.0

0

2.7 ‘)

0

6.4 4.8

0 8.3 7.6 6.2

a(1 5” -j 60”) exp. talc..“)

Relative (d, a)

g g

2

g ?

F

ir

u

g $

8

2

0+2(21)

P ?

4(99) 2(99) 0+2(55)

‘)

L( % mixing) talc. “)

%

36Ar(d, a)34C1 REACTION

45

the others by at least a factor of 103. On the other hand for the 0.15 MeV level reasonably low x2 values are obtained. The relative quality of fits is indicated in the figure by the three horizontal lines drawn for each state. These lines represent probability values of 0.02,O.Ol and 0.001 relative to the probability at the minimum point on the curve. The extracted L-values, L-mixing and the associated errors determined with Cline’s procedure 21) for a 75 y0 confidence limit are listed in table 2. Calculation of the relative (d, N) cross sections with the DWBA is model dependent and requires the use of appropriate mixed configuration two-nucleon structure factors. These structure factors are linear combinations of the pure configuration two-nucleon structure factors, the particular combination being determined by the model wave functions ’ “). In the present investigation, the available s+-d+ shell-model wave functions of Glaudemans 12) were used. 4. Results The present results are summarized and compared with other available data in table 2. The present excitation energies agree within the experimental errors with the accurate previous data. The cl-particle group observed at 3.64 MeV is due to a multiplet of states and no detailed analysis of this group could be made although fits to the composite group were made (fig. 5). 4.1. THE 1+ STATES

The 1’ states at 0.46, 2.58 and 3.13 MeV were readily identified with the (d, a) reaction due to the relatively strongly structured L = 0+2 angular distributions observed for these states. The 1+ state at 665 keV represents the only case studied where, for a single level, two different L-mixtures, L = O-I2 and L = 2+4, gave equally good fits to the data. The L = 0+2 (J"= 1’) angular distribution observed for the level at 2.38 MeV is in a disagreement with the previous angular correlation measurements ‘*“) which have established the spin as J” = 4+. The pure L = 4 transition which would be required for a spin 4+ final state is definitely excluded by our measurements as can be seen in figs. 3, 4 and 5. In view of the general success in identifying other 1’ states, there is a possibility that a doublet exists at about 2.38 MeV in 34C1. The suppression by the (d, a) reaction of the 4+ state relative to the l+ is reasonable considering that the 4’ configuration cannot be excited by a direct deuteron pick-up from the s+-df shell and in absence of any significant configuration admixture should not be seen. 4.2. THE 2+ STATES

Two 2+, T = 0 states are definitely known 51‘) in 34C1 up to 3.38 MeV excitation. The (d, a) transition to the lower state at 1.23 MeV is consistent with the expected pure L = 2. The other 2+ state at 1.89 MeV could not be resolved from the 1.92 MeV

46

R. N. HOROSHKO

AND

M. H. SHAPIRO

state observed weakly by Erskme et al. “) in their 33S(3He, d)34C1 reaction studies. The existence of the 1.92 MeV level is evident in the (d, oz)reaction from the effect it has on the angular distribution of the composite group. The deviation from the pure L = 2 pattern (figs. 4, 5) indicates that the 1.92 MeV level is not 2+. Possible spin values are discussed in subsect. 4.3. 4.3. THE

J= 2 3+ STATES

Only one 3+ state at 0.15 MeV is definitely known in 34C1from many previous investigations. The pure L = 4 angular distribution observed for this state in the (d, CX) reaction is consistent with this .I” value. The unresolved 1.89 (2+)-1.92 MeV doublet is characterized by a mixed L = 2+4 transfer (table 2) provided that positive parity is assumed for the upper member as is suggested by the observed 2 = (2) transition to this state in the 33S(3He, d) reaction ‘). Under these conditions the possible spins for the 1.92 MeV level are 3+, 4” or 5+ with 3+ favored since this value would agree with the (3He, d) measurement “). If on the other hand the parity were negative, no definite statement could be made on the basis of the present data. The 2.18 MeV level is observed with a mixed L = 2 +4 angular distribution indicating J” = 3+ although the errars in L-mixing are such [(87+20)% (L = 4)] that a pure L = 4 and therefore .7” = 4+ or 5+ cannot be excluded. Nevertheless only the 3+ value is consistent with previous y-ray studies ‘* “). The known ‘, ‘) 4’ state at 2.38 MeV was not observed in the present investigation (see subsect 4.1). 4.4. THE

NEGATIVE-PARITY

STATES

The lowest negative-parity state is observed at 2.72 MeV with a mixed L = 1 (81+20) % -1-3 angular distribution (figs. 4, 5) which favors J” = 2- in agreement with other measurements listed in table 2. For the 3.33 MeV level an L = 3 (100+40) % angular distribution is observed (fig. 4) and is favored over other possible L-values by a factor of over 100. The favored spin values for this state are therefore 2-, 3- or 4-. This parity is in disagreement with the possible 1 = (2) transition observed to this state in the 33S(3He, d) reaction “). 4.5. THE

T = 1 STATES

The isospin selection rule AT = 0 forbids the excitation of T = 1 states by the direct 36Ar(d, CX)reaction and, within the accuracy of present measurements limited mainly by the experimental resalution, this selection rule appears to be satisfied at forward angles far the T = 1, 2+ state at 3.38 MeV. However, as is shown in fig. 2, at a relatively large angle of 85” where the reaction may not be entirely direct, this state is seen to be excited with intensity comparable to that of many T = 0 states. The T = 1,2+ state at 2.16 MeV was not seen. With the present resolution of about 75 keV this state could not have been resolved from the 2.18 MeV group.

36Ar(d, a)34CI REACTION

47

The T = 1, O+ ground state was excited very weakly at all angles measured. This is illustrated in fig. 2 for 30”. The observed integrated cross section (lY-60”) is at least two orders of magnitude below the cross sections for most T = 0 states as is shown in table 2. This weakness of the ground state transition cannot, however, be attributed to the isospin selection rule since in addition the parity selection rule prohibits the excitation of the O+ states. 5. Discussion The strong L-dependent structure observed for many angular distributions enabled reasonably definite J” identifications to be made for the l+ states at 0.46, 2.58 and 3.13 MeV, all of which are consistent with previous data listed in table 2. On the same basis we find J” = 1 + for the 2.38 MeV level. This is in contradiction to the previous and quite definite 4+ assignments ‘* ’ ). The nature of the disagreement is discussed in subsect. 4.1, and it appears that an existence of a doublet at about 2.38 MeV is likely. For the 2.18 and 2.72 MeV levels the most likely J” values of 3+ and 2- are not as definite as in the case of the 1+ states, although these values are consistent with other available data noted in the table. DelVecchio et al. “) m ’ t h elr st u d ies of the 52Cr(d, a)“V reaction note that for a contribute, the lower L-value should pure (j’ )J=odd configuration where two L-values dominate. In our case a likely example of such a pure configuration is expected to be the 3 + state at 0.15 MeV which is predicted by Glaudemans 12) to be 98 % (d+)‘. We find however, that the higher L-value, L = 4, dominates which is in agreement with the DWBA calculations using Glaudeman’s wave functions. The L-mixing values and the relative experimental and calculated cross section integrated from 15” to 60” are also shown in table 2. A relative normalization was chosen to give an approximate correspondence between the measured and calculated cross sections for the low-lying states. The relative cross sections and L-mixing are seen to be calculated reasonably well for the l:, 2: and 3: states, while for the 1: state the calculation is significantly worse. Within the framework of the s+-d+ shell model, the (d, U) reaction may populate the 3+ states by a pick-up from the d, orbit only. Thus the 3& states which, according to Glaudemans 12) have only small di components are predicted to be weakly excited, whereas the observed excitation of the possible 3;. 3 states is relatively strong and is indicative of the need to consider other configurations in the model. Ambiguities in the spin assignments for some of the higher levels precluded any further comparison of the relative cross sections with the model predictions. The authors wish to thank Dr. D. Shreve for valuable discussions and helpful comments. They are also grateful to Mr. A. N. Petersen and his crew for efficient operation of the accelerator.

48

R. N. HOROSHKO

AND M. H. SHAPIRO

References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23)

W. W. Daehnick and Y. S. Park, Phys. Rev. Lett. 20 (1968) 110 W. W. Daehnick and Y. S. Park, Phys. Rev. 180 (1969) 1062 Y. S. Park and W. W. Daehnick, Phys. Rev. 180 (1969) 1082 J. R. Hall, J. J. Schwartz and B. A. Watson, Bull. Am. Phys. Sot. 14 (1969) 1201, and private communication J. R. Erskine, D. Crozier, J. P. Schiffer and W. P. Alford, Phys. Rev. C3 (1971) 1976 B. H. Wildenthal, G. M. Crawley and W. McLatchie, Bull. Am. Phys. Sot. 15 (1970) 484 P. M. DeLuca, J. C. Lawson and P. R. Chagnon, Bull. Am. Phys. Sot. 15 (1970) 566, and private communication D. H. Sykes, Nucl. Phys. Al49 (1970) 418 F. Brandolini, I. Filosofo, C. Signorini and M. Morando, Nucl. Phys. Al49 (1970) 401 H. D. Gaber and G. I. Harris, Phys. Rev. 188 (1969) 1685 H. Brunader, J. C. Hardy and J. Cerny, Nucl. Phys. Al37 (1969) 487 P. W. M. Glaudemans, G. Wiechers and P. J. Brussaard, Nucl. Phys. 56 (1964) 529, 548 F. C. Em& Nucl. Phys. 84 (1966) 91 R. W. Zurmiihle and C. M. Fou, Nucl. Instr. 54 (1967) 151 F. Brandolini, R. G. R. Engmann and C. Signorini, Nucl. Phys. Al49 (1970) 411 E. A. Silverstein, Nucl. Instr. 4 (1959) 53 P. D. Kunz, The program DWUCK, University of Colorado, unpublished N. K. Glendenning, Phys. Rev. 137 (1965) B102, Lawrence Radiation Laboratory reports UCRL-18225 (1968), UCRL-18270 (1968) C. M. Perey and F. G. Perey, Phys. Rev. 152 (1966) 923 L. McFadden and G. R. Satchler, Nucl. Phys. 84 (1966) 177 D. Cline and P. M. S. Lesser, Nucl. Instr. 82 (1970) 291 R. DelVecchio et al., Phys. Rev. C3 (1971) 1989 P. M. Endt and C. van der Leun, Nucl. Phys. A105 (1967) 1