- Email: [email protected]
The lowest negative parity state in 21Na
2.G
I
Nuclear Physics A146 (1970) 390--396; (~) North-HollandPublishing Co., Amsterdam Not to be reproduced by photoprlnt or microfilm without written permission from the publisher
THE LOWEST NEGATIVE PARITY STATE IN 2XNa J. E. C H R I S T I A N S S O N ,
J. D U B O I S
and L. 3 A R N E B O K N
Institute of Physics, Chalmers University of Technology and University of Gb'teborg, Gb'teborg, Sweden Received 17 N o v e m b e r 1969 (Revised 15 February 1970) Abstract: The =°Ne(d, n)2~Na reaction has been studied at Ea -~ 4.5 MeV. The neutron angular
distributions indicate [p = 0 and 1 for the 2.41 and 2.79 MeV levels, respectively. The 2.79 MeV leve! is interpreted as the head of a rotational b a n d based on Nilsson orbit ~-- [1011. E [
I
NUCLEAR
R E A C T I O N S Z°Ne(d, n), E = 4.5 MeV; measured cr(En, 0). 21Na deduced levels, lp. Enriched target.
1. Introduction Several investigations oll low-lying levels in 21Na have been reported earlier 1). The main information comes from studies of proton induced resonance reactions on Z°Ne and the Z°Ne(d, n)2~Na reaction. Ajzenberg-Selove et al. z) studied the latter reaction in some detail by measuring time-of-flight spectra of the emitted neutrons at bombarding energies between 2.4 and 6.1 MeV. The angular distributions showed strong direct interaction features. Analysis in terms of the DWBA method a) resulted in the determination of several orbital momenta for low-lying levels in ZtNa. Ajzenberg-Selove et al. z) then suggested that there should be two close-lying ½+ levels in Z~Na, one at 2.43 and the other at 2.83 MeV. This does however not check with recent information 4, s) on Z3Na and 23Mg nuclei, which are expected to have the same level structure as "~lNa and its mirror nucleus ZtNe. For atNa one would like to see only one low-lying ½+ level and close to that an odd parity level. Since the 2.43 MeV level was much more strongly populated in the (d, n) reaction than the 2.83 MeV level it might have severely influenced the measurement of the angular distribution to the latter level. Although it seems to be a nicely performed experiment we thought it worthwhile to check this special part. Since we had no access to significantly better experimental facilities or analysing techniques we had to devote great care in the experimental procedure in order to try to improve the result. Furthermore, it is suggested from the above mentioned systematics that there also should appear a 9+ level in the 2.8 MeV excitation region of ZtNa. After the experimental part of this investigation was finished Pronko et aI. 6) reported on a study of the Z4Mg(p, 0'.)Z~Na reaction with 17.5 MeV protons. The alpha-particle group at 2.83 MeV appeared to be too broad to be a singlet, so they claim that the group feeds a close doublet at 2833.8 __+4.0 and 2803.5 _+5.0 keV. The aim of the present investigation is to prove that one of these levels in ZlNa is an odd parity state. 390
2tNa NEGATIVE PARITY STATE
391
2. Experimental procedure The experimental part of the present investigation was performed at the 5.5 MV Van de Graaff generator at Studsvik. The terminal pulsing system delivered deuteron pulses with a length of about 1 ns at a frequency of 1 MHz. The conventional timeof-flight technique was used. The neon target nuclei were contained in a small gold depleted gas-cell with a 2.5 #m thick Ni foil facing the incoming deuteron beam. The gas was enriched in Z°Ne to 99.95 }0 and the pressure in the cell was kept at a constant value of about 50 mm Hg. After covering the flight path of 8 m the emitted neutrons were detected by means of a 12.5 cm in diameter and 2.5 cm thick liquid scintillator. The bias of the slow signal from the detector was set to record neutrons with energies equal to or larger than 1 MeV. Two fast signals, derived from the photomultiplier anode and from the beam pulse pick-off tube, provided start and stop pulses for a time-to-pulse-height converter. The time-of-flight spectra were recorded in 256 channels of a pulse-height analyser. Spectra were measured at angles between 0 ° and 40 ° in steps of 5 ° for the same amount of incident beam charge. In order to obtain the background, spectra were also recorded with the gas cell evacuated. Of course this background did not include the neutrons primarily produced in the 2°Ne(d, n)21Na reaction and then scattered in the surrounding material before reaching the detector. That uncertainty of the background caused the main error in the determination of the areas under the neutron peaks. The energy calibration was obtained from the identification of the 7-peak and the intensive neutron group to the 2.41 MeV level in ZlNa 1). As a further check of the energy calibration, accurately known delays were incorporated in the fast electronic circuits and the shifts of the peaks were measured.
3. Experimental results and analysis The Z°Ne(d, n)/1Na reaction was studied at an average deuteron energy of 4.5 MeV. A typical time-of-flight spectrum with the background subtracted is shown in fig. 1. The identification of the groups from the 2°Ne(d, n)ZlNa reaction was made from the runs at all the angles. If we use the recommended average energy of 2.409+_0.010 MeV [ref. 1)] for the 2.43 MeV level we obtain 2.79 -t-0.01 MeV for the level of interest in this investigation. The neutron groups to these two levels are completely resolved. The angular distributions are extracted from the time spectra by determination of the areas under the neutron peaks (figs. 2 and 3). The limited space in the laboratory did not permit us to measure beyond 40 ° . The pronounced forward peaking of the angular distribution suggests that direct transition processes between the initial and final states are the dominating reaction mechanism. Theoretical calculations of the differential cross section as a function of angle can then be obtained from the optical model. Zero range DWBA calculations
J. 1~, CHRISTIANSSONeta/.
392
were carried out by means of the code JULIE of Bassel, Drisko and Satchler 7). This code uses bound state wave functions calculated from the Schr6dinger equation by adjusting the well depth of a Saxon-Wood potential. The values of radius and diffuseness parameter of the shape of the potential were those recommended by Bassel Channel
50
1O0
Counts
150
I
L
20
2.41
21
Ne(d,n) Na Ed=4.5NeV 8
t eb
= 20 °
0.34 + G.S.
I03
1,70
1( o
g o~S ~ o
o
102
ooo
o
3
2
% coo
4
Neutron
5 6 7 energy (MeV)
Fig. I. N e u t r o n s p e c t r u m with b a c k g r o u n d s u b t r a c t e d observed at 20 ° f r o m the 2°Ne(d, n ) 2 t N a r e a c t i o n at an average deuteron b e a m energy o f 4.5 MeV. T h e figures attached to the n e u t r o n p e a k s are the excitation energies in M e V o f the p o p u l a t e d levels in 21Na.
et al. 7). Furthermore the optical potential for the incident deuteron waves was taken
to be of the form V
vd=v~
W
i r--R
1 + exp - a
r--R
1 + exp - a
+it2 16;1 1 \re,c/
V~.o. -
r drr
+exp
r - -aR
l.a,
21Na NEGATIVEPARITYSTATE
.-° c
[
20
393
21
I Ne (d,n) Na s xl0~ ~E~ = 4.SMeV =~ ~ . - - - - " - . x E N Q = 2.41 MeV
.~ 2xl 0s -~ m
~ experiment
I 0s
£p:O,DWBA 1,DWBA
g ~
5x 10~
\-'--
2 xlO~
\
0°
1
i
i
I
I
10"
20"
30 °
40 °
50"
ecM
Fig. 2. Angular distributions of the neutron group from the ~°Ne(d, n ) : l N a reaction leading to the 2.41 MeV level in ZlNa at an average deuteron energy o f 4.5 MeV. Open circles with associated errorbars are experimental values proportional to the differential cross section and the curves are the DWBA prediction for lp = 0 and Ip = 1 fitted to the experimental values.
g 2X103 ~_ 2°Ne(d,n )21Na :~ : ~ ~- i Ed=A'SMeV ,0' ~ ' ~ ~-"k E2.: 2.79MeV ~o
5 X'102
\ \
2 x 10 =
~ experiment \ ----
3[p= 1, D W B A £p=0,DWBA
10 2
5x101
I 0°
i
I
10 ° 20 Q 30 °
i
i
1.0°
50 °
Fig. 3. Angular distributions of the neutron group from the :°Ne(d, n)21Na reaction leading to the 2.79 MeV level in 21Na at an average deuteron energy of 4.5 MeV. Open circles with associated errorbars are experimental values proportional to the differential cross section and the curves are the DWBA predictions for lp = 0 and l~ = 1 fitted to the experimental values.
w i t h t h e f o l l o w i n g p a r a m e t e r s 8): a=0.7
fro, R = r 0
V = 95 M e V ,
W = 10 M e V ,
V~.o. = 6 M e V ,
A~ w i t h r0 = 1.35 f m a n d Vc e q u a l t o t h e p o t e n t i a l f r o m a
J.E. CHRISTIANSSONetal.
394
uniformly charged sphere with the radius r c A ~ where rc = 1.25 fm. For the outgoing neutron waves the potential
Un-
V
+iV/,a,Id_
1 + exp r _ _R -
dr
1 zsR~] 1 + exp
a
a
was used with the parameters given by Wilmore and Hodgson 9); V = 46 MeV, = 37 MeV, r 0 = 1.31 fm, r~ = 1.26 fm, a = 0.66 fm and a' = 0.48 fro. No contribution from compound nuclear formation was included in the theoretical calculations. In figs. 2 and 3 the calculations have been fitted to the experimental angular distributions and evidently good fits are obtained for lp = 0 and lp = 1 for the 2.41 and 2.79 MeV levels respectively.
W'
Me~
......
~
312~ s/2' .,,..,.~
. . . . .
2
,.,
21
Ne
I ._J~tz- 50~] |
_~/2"[2,]
_-
21
23
Ne
23
Mg
312" [211]
23
Ne
Ne
Exp.
Theory
Fig. 4. Comparison of low-lying leveis in 2ZNe, 2tNa, 23Mg and 23Na. These nuclei all having the odd member of protons or neutrons equal to 11, are supposed to have almost identical level schemes. The theoretical calculation of the levels in 2SNa using the Nilsson model is from the work of Dubois % The experimental results obtained in the present investigation are included for 2tNa together with information on nuclear data from the compilation by Endt and Van der Leun 1). Additional data on the levels in 2ZNe and ~ N a are from Bloch et al, 12) and Pronko e t a l . 6) and in Z3Na and ZSMg from Dubois 4) and Dubois and Earwaker 2) respectively.
As was pointed out above, it has been suggested 6) that there should be two levels in a n n a around 2.8 MeV i.e. at 2833.8_+_+4.0 and 2803.5_+5.0 keV. These energies are, however, quoted in an energy scale which is about 20 keV higher than the one used in the present investigation. Since the energy of the 2.79 MeV was reproduceable within 10 keV relative to the 2.409 MeV level we are certain that mainly the lower lying level of the doublet was
2~Na NEGATIVE PARITY STATE
395
populated. Then the higher-lying level is probably a ~+ state and it would require four units of angular momentum transfer to be populated. DWBA calculations and experiences from the study of the 22Ne(3He, d)23Na reaction 4) suggest that it would result in a comparatively small differential cross section and an angular distribution slowly rising as a function of angle. This is in strong contrast to what experimentally was found for the 2.79 Me¥ level studied (fig. 4). However, at 40 ° the yield is somewhat higher than expected from a pure lp = 1 distribution and that might indicate some contribution from the higher-lying level. The energy of the level obtained at this angle was in fact slightly higher (2.80 MeV) than we obtained at the smaller angles (2.79 MeV). All experimental facts favour the interpretation that it is really the 2.79 MeV (2803.5 keV) level, which is the Ip = I state. 4. Discussion
The Nilsson diagram 1o) suggests that the lowest-lying odd-parity states can be found in odd-mass nuclei with 11 neutrons or protons by promoting the odd particle from orbit 7 (3 + [211]) into orbit 14 (½- [330]) or by lifting a particle up from orbit 4 (½- [101 ]) to pair off with the odd particle in orbit 7. Rotational bands can then be based on these particle and hole states. Such bands have been identified in 23Mg and 23Na [refs. 4, 5)]. These experiments point out the hole character of the lowest oddparity levels. Furthermore the experimental level spacings between the presumed numbers of the band are in reasonably good agreement with theory if the band is based on the hole state i.e. orbit 4. This is not at all the case if the band is based on the particle state i.e. orbit 14. On the other hand the calculated excitation energy for a particle in orbit 4 in a deformed well turns out to be considerably higher than the experimental value of 2.79 MeV. However, the situation might be improved if particle-hole pairing and p-n interaction energy are included. Recently calculations have been done at Stony Brook by Blomqvist 11), who shows that in this way quite a lot of energy is gained, when a proton in the odd-A T1 and Bi isotopes is excited across thegap from3s~to lh~. Energy considerations and the hole character of the levels thus strongly favour the identification of the low-lying odd-parity states in 23Mg and 23Na being members of rotational bands based on orbit 4. The 2.79 MeV level in 21Na, which in the present investigation has been proved to be either a ½- or a 3- state, should then be the head of the corresponding band in this nucleus. It shows the hole character by being populated very weakly in comparison with the 2.41 MeV level (fig. 1), which should be the particle state based on the ½+ [211] orbit. Recently Bloch et al. 12) investigated several narrow resonances in the proton bombardment of 2°Ne and found that the levels at 3.68 and 3.86 MeV in 21Na had spins and parities oi~es - and {- respectively. They tried in vain to fit their experimental data, assuming these two levels to be the lowest members of a rotational band based
396
J . E . CI-IRISTIANSSON et al.
on orbit 14 and therefore concluded that the 3.680 M e V and 3.864 MeV states do not seem to be related to Nilsson states. However, f r o m the discussion above it is obvious that these two levels can very well be the second and third member of the rotational b a n d based on the Ip = 1 level at 2.79 MeV. As a s u m m a r y we have in fig. 4 drawn the experimental level schemes o f lowlying levels in the 21Ne, 21Na, 23Mg and 23Na nuclei together with theoretical level scheme of 23Na as it has been obtained by Dubois 4) when band mixing was included in the calculations for the positive parity states. One is able to identify corresponding levels in the different nuclei although some u n a m b i g u o u s spin and parity assignments still are missing. However, the second member o f the b a n d based on the ½+ [211] orbit can n o t be identified in either 21Na or in 21No. It might be revealed in 21Na if the 2°No(d, n)Z~Na reaction is studied at higher bombarding energies then we used in the present investigation. The authors gratefully acknowledge the technical assistance of the Van de Graaff g r o u p at Studsvik and fil. lic. L. Nilsson. We also thank Prof. N. Ryde for his kind interest.
References 1) P. M. Endt and C. van der Leun, Nucl. Phys. A105 (1967) 11 2) F. Ajzenberg-Selove, L. Crar~berg and F. S. Dietrich, Phys. Rev. 124 (1961) 1548 3) W. Tobocman, Phys. Rev. 115 (1959) 98 4) J. Dubois, Nucl. Phys. A104 (1967) 657 5) J. DLlbois and L. G. Earwaker, Phys. Rev. 160 (1967) 925 6) J. G. Pronko, R. A. Lindgren and D. A. Bromley, A140 (1970) 465 7) R. I-I. Bassel, R. M. Drisko and G. R. Satchler, ORNL-3240, unpublished 8) H. Fuchs, K. Grabisch, P. Kraaz and G. R6schert, Nucl. Phys. A10] (1967) 590 9) D. Wilmore and P. E. Hodgson, Nucl. Phys. 55 (1964) 673 I0) S. G. Nilsson, Mat. Fys. Medd. Dan. Vid. Selsk. 29, No. 16 (1955) 11) J. Blomqvist, private communication 12) R. Bloch, T. Knellwo|f and R. E. Pixley, Nucl. Phys. A123 (1969) 129
I
Nuclear Physics A146 (1970) 390--396; (~) North-HollandPublishing Co., Amsterdam Not to be reproduced by photoprlnt or microfilm without written permission from the publisher
THE LOWEST NEGATIVE PARITY STATE IN 2XNa J. E. C H R I S T I A N S S O N ,
J. D U B O I S
and L. 3 A R N E B O K N
Institute of Physics, Chalmers University of Technology and University of Gb'teborg, Gb'teborg, Sweden Received 17 N o v e m b e r 1969 (Revised 15 February 1970) Abstract: The =°Ne(d, n)2~Na reaction has been studied at Ea -~ 4.5 MeV. The neutron angular
distributions indicate [p = 0 and 1 for the 2.41 and 2.79 MeV levels, respectively. The 2.79 MeV leve! is interpreted as the head of a rotational b a n d based on Nilsson orbit ~-- [1011. E [
I
NUCLEAR
R E A C T I O N S Z°Ne(d, n), E = 4.5 MeV; measured cr(En, 0). 21Na deduced levels, lp. Enriched target.
1. Introduction Several investigations oll low-lying levels in 21Na have been reported earlier 1). The main information comes from studies of proton induced resonance reactions on Z°Ne and the Z°Ne(d, n)2~Na reaction. Ajzenberg-Selove et al. z) studied the latter reaction in some detail by measuring time-of-flight spectra of the emitted neutrons at bombarding energies between 2.4 and 6.1 MeV. The angular distributions showed strong direct interaction features. Analysis in terms of the DWBA method a) resulted in the determination of several orbital momenta for low-lying levels in ZtNa. Ajzenberg-Selove et al. z) then suggested that there should be two close-lying ½+ levels in Z~Na, one at 2.43 and the other at 2.83 MeV. This does however not check with recent information 4, s) on Z3Na and 23Mg nuclei, which are expected to have the same level structure as "~lNa and its mirror nucleus ZtNe. For atNa one would like to see only one low-lying ½+ level and close to that an odd parity level. Since the 2.43 MeV level was much more strongly populated in the (d, n) reaction than the 2.83 MeV level it might have severely influenced the measurement of the angular distribution to the latter level. Although it seems to be a nicely performed experiment we thought it worthwhile to check this special part. Since we had no access to significantly better experimental facilities or analysing techniques we had to devote great care in the experimental procedure in order to try to improve the result. Furthermore, it is suggested from the above mentioned systematics that there also should appear a 9+ level in the 2.8 MeV excitation region of ZtNa. After the experimental part of this investigation was finished Pronko et aI. 6) reported on a study of the Z4Mg(p, 0'.)Z~Na reaction with 17.5 MeV protons. The alpha-particle group at 2.83 MeV appeared to be too broad to be a singlet, so they claim that the group feeds a close doublet at 2833.8 __+4.0 and 2803.5 _+5.0 keV. The aim of the present investigation is to prove that one of these levels in ZlNa is an odd parity state. 390
2tNa NEGATIVE PARITY STATE
391
2. Experimental procedure The experimental part of the present investigation was performed at the 5.5 MV Van de Graaff generator at Studsvik. The terminal pulsing system delivered deuteron pulses with a length of about 1 ns at a frequency of 1 MHz. The conventional timeof-flight technique was used. The neon target nuclei were contained in a small gold depleted gas-cell with a 2.5 #m thick Ni foil facing the incoming deuteron beam. The gas was enriched in Z°Ne to 99.95 }0 and the pressure in the cell was kept at a constant value of about 50 mm Hg. After covering the flight path of 8 m the emitted neutrons were detected by means of a 12.5 cm in diameter and 2.5 cm thick liquid scintillator. The bias of the slow signal from the detector was set to record neutrons with energies equal to or larger than 1 MeV. Two fast signals, derived from the photomultiplier anode and from the beam pulse pick-off tube, provided start and stop pulses for a time-to-pulse-height converter. The time-of-flight spectra were recorded in 256 channels of a pulse-height analyser. Spectra were measured at angles between 0 ° and 40 ° in steps of 5 ° for the same amount of incident beam charge. In order to obtain the background, spectra were also recorded with the gas cell evacuated. Of course this background did not include the neutrons primarily produced in the 2°Ne(d, n)21Na reaction and then scattered in the surrounding material before reaching the detector. That uncertainty of the background caused the main error in the determination of the areas under the neutron peaks. The energy calibration was obtained from the identification of the 7-peak and the intensive neutron group to the 2.41 MeV level in ZlNa 1). As a further check of the energy calibration, accurately known delays were incorporated in the fast electronic circuits and the shifts of the peaks were measured.
3. Experimental results and analysis The Z°Ne(d, n)/1Na reaction was studied at an average deuteron energy of 4.5 MeV. A typical time-of-flight spectrum with the background subtracted is shown in fig. 1. The identification of the groups from the 2°Ne(d, n)ZlNa reaction was made from the runs at all the angles. If we use the recommended average energy of 2.409+_0.010 MeV [ref. 1)] for the 2.43 MeV level we obtain 2.79 -t-0.01 MeV for the level of interest in this investigation. The neutron groups to these two levels are completely resolved. The angular distributions are extracted from the time spectra by determination of the areas under the neutron peaks (figs. 2 and 3). The limited space in the laboratory did not permit us to measure beyond 40 ° . The pronounced forward peaking of the angular distribution suggests that direct transition processes between the initial and final states are the dominating reaction mechanism. Theoretical calculations of the differential cross section as a function of angle can then be obtained from the optical model. Zero range DWBA calculations
J. 1~, CHRISTIANSSONeta/.
392
were carried out by means of the code JULIE of Bassel, Drisko and Satchler 7). This code uses bound state wave functions calculated from the Schr6dinger equation by adjusting the well depth of a Saxon-Wood potential. The values of radius and diffuseness parameter of the shape of the potential were those recommended by Bassel Channel
50
1O0
Counts
150
I
L
20
2.41
21
Ne(d,n) Na Ed=4.5NeV 8
t eb
= 20 °
0.34 + G.S.
I03
1,70
1( o
g o~S ~ o
o
102
ooo
o
3
2
% coo
4
Neutron
5 6 7 energy (MeV)
Fig. I. N e u t r o n s p e c t r u m with b a c k g r o u n d s u b t r a c t e d observed at 20 ° f r o m the 2°Ne(d, n ) 2 t N a r e a c t i o n at an average deuteron b e a m energy o f 4.5 MeV. T h e figures attached to the n e u t r o n p e a k s are the excitation energies in M e V o f the p o p u l a t e d levels in 21Na.
et al. 7). Furthermore the optical potential for the incident deuteron waves was taken
to be of the form V
vd=v~
W
i r--R
1 + exp - a
r--R
1 + exp - a
+it2 16;1 1 \re,c/
V~.o. -
r drr
+exp
r - -aR
l.a,
21Na NEGATIVEPARITYSTATE
.-° c
[
20
393
21
I Ne (d,n) Na s xl0~ ~E~ = 4.SMeV =~ ~ . - - - - " - . x E N Q = 2.41 MeV
.~ 2xl 0s -~ m
~ experiment
I 0s
£p:O,DWBA 1,DWBA
g ~
5x 10~
\-'--
2 xlO~
\
0°
1
i
i
I
I
10"
20"
30 °
40 °
50"
ecM
Fig. 2. Angular distributions of the neutron group from the ~°Ne(d, n ) : l N a reaction leading to the 2.41 MeV level in ZlNa at an average deuteron energy o f 4.5 MeV. Open circles with associated errorbars are experimental values proportional to the differential cross section and the curves are the DWBA prediction for lp = 0 and Ip = 1 fitted to the experimental values.
g 2X103 ~_ 2°Ne(d,n )21Na :~ : ~ ~- i Ed=A'SMeV ,0' ~ ' ~ ~-"k E2.: 2.79MeV ~o
5 X'102
\ \
2 x 10 =
~ experiment \ ----
3[p= 1, D W B A £p=0,DWBA
10 2
5x101
I 0°
i
I
10 ° 20 Q 30 °
i
i
1.0°
50 °
Fig. 3. Angular distributions of the neutron group from the :°Ne(d, n)21Na reaction leading to the 2.79 MeV level in 21Na at an average deuteron energy of 4.5 MeV. Open circles with associated errorbars are experimental values proportional to the differential cross section and the curves are the DWBA predictions for lp = 0 and l~ = 1 fitted to the experimental values.
w i t h t h e f o l l o w i n g p a r a m e t e r s 8): a=0.7
fro, R = r 0
V = 95 M e V ,
W = 10 M e V ,
V~.o. = 6 M e V ,
A~ w i t h r0 = 1.35 f m a n d Vc e q u a l t o t h e p o t e n t i a l f r o m a
J.E. CHRISTIANSSONetal.
394
uniformly charged sphere with the radius r c A ~ where rc = 1.25 fm. For the outgoing neutron waves the potential
Un-
V
+iV/,a,Id_
1 + exp r _ _R -
dr
1 zsR~] 1 + exp
a
a
was used with the parameters given by Wilmore and Hodgson 9); V = 46 MeV, = 37 MeV, r 0 = 1.31 fm, r~ = 1.26 fm, a = 0.66 fm and a' = 0.48 fro. No contribution from compound nuclear formation was included in the theoretical calculations. In figs. 2 and 3 the calculations have been fitted to the experimental angular distributions and evidently good fits are obtained for lp = 0 and lp = 1 for the 2.41 and 2.79 MeV levels respectively.
W'
Me~
......
~
312~ s/2' .,,..,.~
. . . . .
2
,.,
21
Ne
I ._J~tz- 50~] |
_~/2"[2,]
_-
21
23
Ne
23
Mg
312" [211]
23
Ne
Ne
Exp.
Theory
Fig. 4. Comparison of low-lying leveis in 2ZNe, 2tNa, 23Mg and 23Na. These nuclei all having the odd member of protons or neutrons equal to 11, are supposed to have almost identical level schemes. The theoretical calculation of the levels in 2SNa using the Nilsson model is from the work of Dubois % The experimental results obtained in the present investigation are included for 2tNa together with information on nuclear data from the compilation by Endt and Van der Leun 1). Additional data on the levels in 2ZNe and ~ N a are from Bloch et al, 12) and Pronko e t a l . 6) and in Z3Na and ZSMg from Dubois 4) and Dubois and Earwaker 2) respectively.
As was pointed out above, it has been suggested 6) that there should be two levels in a n n a around 2.8 MeV i.e. at 2833.8_+_+4.0 and 2803.5_+5.0 keV. These energies are, however, quoted in an energy scale which is about 20 keV higher than the one used in the present investigation. Since the energy of the 2.79 MeV was reproduceable within 10 keV relative to the 2.409 MeV level we are certain that mainly the lower lying level of the doublet was
2~Na NEGATIVE PARITY STATE
395
populated. Then the higher-lying level is probably a ~+ state and it would require four units of angular momentum transfer to be populated. DWBA calculations and experiences from the study of the 22Ne(3He, d)23Na reaction 4) suggest that it would result in a comparatively small differential cross section and an angular distribution slowly rising as a function of angle. This is in strong contrast to what experimentally was found for the 2.79 Me¥ level studied (fig. 4). However, at 40 ° the yield is somewhat higher than expected from a pure lp = 1 distribution and that might indicate some contribution from the higher-lying level. The energy of the level obtained at this angle was in fact slightly higher (2.80 MeV) than we obtained at the smaller angles (2.79 MeV). All experimental facts favour the interpretation that it is really the 2.79 MeV (2803.5 keV) level, which is the Ip = I state. 4. Discussion
The Nilsson diagram 1o) suggests that the lowest-lying odd-parity states can be found in odd-mass nuclei with 11 neutrons or protons by promoting the odd particle from orbit 7 (3 + [211]) into orbit 14 (½- [330]) or by lifting a particle up from orbit 4 (½- [101 ]) to pair off with the odd particle in orbit 7. Rotational bands can then be based on these particle and hole states. Such bands have been identified in 23Mg and 23Na [refs. 4, 5)]. These experiments point out the hole character of the lowest oddparity levels. Furthermore the experimental level spacings between the presumed numbers of the band are in reasonably good agreement with theory if the band is based on the hole state i.e. orbit 4. This is not at all the case if the band is based on the particle state i.e. orbit 14. On the other hand the calculated excitation energy for a particle in orbit 4 in a deformed well turns out to be considerably higher than the experimental value of 2.79 MeV. However, the situation might be improved if particle-hole pairing and p-n interaction energy are included. Recently calculations have been done at Stony Brook by Blomqvist 11), who shows that in this way quite a lot of energy is gained, when a proton in the odd-A T1 and Bi isotopes is excited across thegap from3s~to lh~. Energy considerations and the hole character of the levels thus strongly favour the identification of the low-lying odd-parity states in 23Mg and 23Na being members of rotational bands based on orbit 4. The 2.79 MeV level in 21Na, which in the present investigation has been proved to be either a ½- or a 3- state, should then be the head of the corresponding band in this nucleus. It shows the hole character by being populated very weakly in comparison with the 2.41 MeV level (fig. 1), which should be the particle state based on the ½+ [211] orbit. Recently Bloch et al. 12) investigated several narrow resonances in the proton bombardment of 2°Ne and found that the levels at 3.68 and 3.86 MeV in 21Na had spins and parities oi~es - and {- respectively. They tried in vain to fit their experimental data, assuming these two levels to be the lowest members of a rotational band based
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on orbit 14 and therefore concluded that the 3.680 M e V and 3.864 MeV states do not seem to be related to Nilsson states. However, f r o m the discussion above it is obvious that these two levels can very well be the second and third member of the rotational b a n d based on the Ip = 1 level at 2.79 MeV. As a s u m m a r y we have in fig. 4 drawn the experimental level schemes o f lowlying levels in the 21Ne, 21Na, 23Mg and 23Na nuclei together with theoretical level scheme of 23Na as it has been obtained by Dubois 4) when band mixing was included in the calculations for the positive parity states. One is able to identify corresponding levels in the different nuclei although some u n a m b i g u o u s spin and parity assignments still are missing. However, the second member o f the b a n d based on the ½+ [211] orbit can n o t be identified in either 21Na or in 21No. It might be revealed in 21Na if the 2°No(d, n)Z~Na reaction is studied at higher bombarding energies then we used in the present investigation. The authors gratefully acknowledge the technical assistance of the Van de Graaff g r o u p at Studsvik and fil. lic. L. Nilsson. We also thank Prof. N. Ryde for his kind interest.
References 1) P. M. Endt and C. van der Leun, Nucl. Phys. A105 (1967) 11 2) F. Ajzenberg-Selove, L. Crar~berg and F. S. Dietrich, Phys. Rev. 124 (1961) 1548 3) W. Tobocman, Phys. Rev. 115 (1959) 98 4) J. Dubois, Nucl. Phys. A104 (1967) 657 5) J. DLlbois and L. G. Earwaker, Phys. Rev. 160 (1967) 925 6) J. G. Pronko, R. A. Lindgren and D. A. Bromley, A140 (1970) 465 7) R. I-I. Bassel, R. M. Drisko and G. R. Satchler, ORNL-3240, unpublished 8) H. Fuchs, K. Grabisch, P. Kraaz and G. R6schert, Nucl. Phys. A10] (1967) 590 9) D. Wilmore and P. E. Hodgson, Nucl. Phys. 55 (1964) 673 I0) S. G. Nilsson, Mat. Fys. Medd. Dan. Vid. Selsk. 29, No. 16 (1955) 11) J. Blomqvist, private communication 12) R. Bloch, T. Knellwo|f and R. E. Pixley, Nucl. Phys. A123 (1969) 129