Some evidence of nuclear shell effects for photoprotons

I1.D.l:2.i I

Nuclear Physics 72 (1965) 305--325; (~) North-Holland Publishin# Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

SOME EVIDENCE OF NUCLEAR S H E L L EFFECTS FOR P H O T O P R O T O N S KATSUFUSA

SHODA t

Ecole Normale Supdrieure, Laboratoire de l'Accdldrateur Lindaire, Orsay, France Received 26 N o v e m b e r 1964 Abstract: T h e energy distributions o f p h o t o p r o t o n s f r o m nuclei between F x8 a n d Z n are discussed

for the residual states. T h e residual states for strong transitions are f o u n d in t h e g r o u n d state for e v e n - p r o t o n nuclei a n d the excited state for o d d - p r o t o n nuclei. T h e cross sections are calculated f r o m energy distributions o f the p h o t o p r o t o n s a s s u m i n g complete transitions o f the a b o v e - m e n t i o n e d residual states. C o m p a r i s o n s are m a d e a n d s o m e evidence for shell effects are found. T h e a n g u l a r distributions do n o t contradict the shell m o d e l u n d e r t h e a s s u m p t i o n o f transition to the a b o v e - m e n t i o n e d residual states. Some c o m p a r i s o n s with o t h e r reactions are also discussed.

1. Introduction

The giant resonance in photonuclear reactions was first explained by the collective motion of nucleons in the nucleus in resonance with gamma-rays 2). The energy distribution of emitted nucleons was expected to be due to their evaporation from excited nuclei in this model. The model did not give a complete explanation for the large photoproton yields observed and for the considerable emission of high energy protons. Courant 2) calculated the process of direct emission of nucleons using a simple square well potential. Burkhardt 3) and Wilkinson 4) also attempted to explain the giant resonance using a nuclear shell model for direct transitions. Their results seemed to explain many aspects of photoreactions, with the exception of the value of the photon energy for the giant resonance. This discrepancy of the resonance energy has been removed by considering the energy shift from particle-hole interactions. Since Brown and Bolsterli 5) established a relation between particle-hole interaction and electric dipole states, many practical calculations have been made for C t2 (ref. 6)), O16 (refs. 7, s)), Ca, O (ref. 7)) and C ~3 (ref. 9)) using this model. The results are in good agreement with the structure of the giant resonances which have been observed recently. However, these calculations are limited to almost closed shell nuclei. Unfortunately, numerical calculations have not been performed for nuclei having many nucleons outside the closed shell because of their complexity. Mihailovi6 and Rosina ~o) calculated the particle-hole effect for non-closed-shell nuclei. According to their calculations, the largest effect is due to the indirect excitat Present address: D e p a r t m e n t o f Physics T o h o k u University, Sendai, Japan. 305

306

K. SHODA

tion of two particle-hole pairs by means of the residual forces between the configurations and the dipole states, which take away some dipole strength from the dipole states of Brown e t al. They considered the contribution of these effects to the broadening of the giant resonance in such unclosed nuclei. If the emission process contains a significant direct interaction, the shell effect will appear in the energy distributions and the angular distributions of the emitted nucleons. The most complete studies were made for O16(7, p) 11) and to a lesser extent for other even nuclei 12). In these results, many structures were found and large transitions to the ground state of residual nuclei were observed 12) compared with the inverse reaction (p, 70). However, some different types of energy distributions were found in (7, P) reaction between even-proton and odd-proton nuclei 13,14). It seems worth while to investigate the modes of disintegration of photonuclear reactions systematically. The mode of disintegration is very characteristic for each of the very light nuclei and also there exist many ambiguities for the discrimination of emitted particles from the reactions (7, t), (7, d), (7, ce) etc. which show substantial yields in these very light nuclei. Many experiments have been successfully performed for lp-shell nuclei, Therefore we have dealt mainly with nuclei of the ld-2s shells and If shells.

2. Relations between the Atomic Number and the Energy of the Residual Levels Strongly Excited by Photoproton Reactions There are many experimental results for energy distributions of photoprotons. They are shown in fig. 1 for those obtained from irradiation with 24 MeV bremsstrahlung under similar conditions (in the same laboratory t). The figure also includes some results obtained from irradiations at the same energy in other laboratories. The abscissa shown is ER -

A-1 A

(Eu~a~-Eth)-Ep,

(1)

where A is the mass number of the target nucleus, Ermax is the maximum photon energy of the bremsstrahlung (Err~ax being 24.0 MeV), Eth is the threshold energy of the reaction, and Ep is the energy of the emitted photoprotons. Then ( A - 1 / A ) ( E r max--Eta) is the maximum proton energy expected from the ground state transition after absorption of a photon of energy Erma~. Therefore, the results are normalized by eq. (1) to the proton energies which should be obtained by the ground state transition after absorption of a photon Ermax. If the assumption is made that the cross section is not zero at this energy, which seems to be valid considering cross sections of neighThe energy scale of the protons in the results at Tohoku University seems to require a slight correction. The figures presented in this paper are the corrected ones. However, these corrections have little effect on our qualitative arguments.

NUCLEAR

SHELL

307

EFFECTS

bouring nuclei ~3), the figure shows that there are two different modes of transition around E~ = 24 MeV. The one is for even-proton nuclei, the spectra of which converge to ER = 0, which suggests that the ground state transition predominates. The

10~ 9

7..~

6~

o

"" 2

/

~u 3

oo~ h I

" ,i- T /

'I° "fir,_t* b, i

~ '~'~ '*

i,

i f oi

t I

I

I~ ~,~

r-'7-

I

I I i

i i I I

I L]

;5

i

i

13

i

i

11

I

I

9

I

i

I

7

E R : A A 1 (E) max - Eth) - Ep

t 5

L

(MeV)

I I LiJ 3

l

I ii i I l-l'i'-~ I la

'

I n I I

t

Fig. 1. T h e energy distributions o f p h o t o p r o t o n s obtained f r o m the irradiation o f 24 M e V bremsstrahlung. T h o s e f r o m similar conditions (in the s a m e laboratory) are s h o w n by plots a n d s m o o t h curves. T h o s e obtained in o t h e r laboratories are s h o w n by histograms. Broken lines s h o w u n c e r t a i n regions considering statistical errors a n d b a c k g r o u n d s . T h e abscissa is ER = ( A - - 1 / A )(E~, raax--Eth) --Ep, w h i c h m e a n s t h e n o r m a l i z a t i o n o f spectra at the p r o t o n energies that s h o u l d be expected by the g r o u n d state transition after a b s o r p t i o n o f a p h o t o n Er max- Distributions for e v e n - p r o t o n nuclei converge to ER = 0 w h i c h m e a n s a considerable g r o u n d state transition exists. T h o s e o f o d d - p r o t o n nuclei converge to ER > 0 w h i c h indicate t h a t t h e g r o u n d state transition is small or does n o t exist. 1. 2aCu ref. 23). 2. 27Co 6a ref. 21). 3. 2~Cu ref. 2a). 4. laK 89 ref. s0). 5. 15Pal ref. 14). 6. xaA127 ref. lg). 7. l l N a ~8 ref. is). 8. 26Fe 5s ref. 17). 9. 16Sa2 ref. 16). 10. u M g 25 ref. 15). 1 1. x4Si2s ref. 14).

308

K. SHODA

TABLE 1 Energies a n d characteristics o f the lowest level in which t h e residual nuclei are left after p r o t o n emission Nucleus

Z

Photon energy a)

Threshold energy

(MeV)

(MeV)

Residual nucleus

F 19

9

19

7.95

018

F 1°

9

17.5 b)

7.95

0

N e s°

10

N a 28

11

<23

c)

24.0

12.84 8.79 8.79

Lowest Energy Character value o f o f lowest o f the Ea residual level residual (MeV) (MeV) level 0

TM

F TM Ne 8z

0 ( ~ 1)

0

ground 0 +

84)

0

ground 0+

a2)

0

g r o u n d ½+

13)

(1.27) 3.35a)

( l s t 2 +) 2 n d l ~ or 2 -

18)

1.27

1st 2 +

,1)

N a °a

11

17.5 b)

M g ~4

12

21.5

11.69

N a sa

0

0

g r o u n d {+

80

M g 25

12

24.0

12.06

N a 84

0

0

ground 4+

15)

A127

13

24.0

8.27

M g 8°

~3.5

3.58

3rd 0

19)

AI or

13

17.5 b)

8.27

M g 88

2.94

2 n d 2+

s0)

Si ns

14

24.0

11.58

A187

g r o u n d ~+

it)

psi

15

24.0

7.29

Si °°

p31

15

19.0

7.29

Si s°

0

0

ground 0+

88)

S 38

16

24.0

8.86

psi

0

0

g r o u n d ½+

le)

S an

16

17.0

8.86

pal

0

K a°

19

24.0

6.37

A ss

K 89

19

17.5 b)

6.37

A 89

Ca 4°

20

20.5

8.34

K 8°

M n 85

25

20.5

8.06

C# 4

Fe ~6

26

24.0

Co sa

27

24.0

7.37

Fe 88

1-2

1.66

Ni ~s

28

25.5

8.17

Co ~

"~0

0

~5

~4.5

10.2

N e 8~

Ref.

M n ~6

C u 83

29

24.0

6.13

Ni °8

C u ss

29

17.5 b)

6.13

NP s

Z n s4

30

20.8

7.71

C u 68

0

0 ~ 7 e)

0 2-3

0 1-2 0

0

it)

g r o u n d ½+

87)

2.16

1st 2 +

80)

2.16

1st 2 +

ss)

0

g r o u n d ~+

8~,88,89)

3rd (4 +)

17)

ground ~-

17)

2nd 2 +

81)

ground {-

88)

0 f)

ground 0 +

at)

0

ground ~-

so)

1.83 0

8~,23)

T h e energies o f t h e p h o t o n s are a r o u n d the m a x i m u m energy o f the b r e m s s t r a h l u n g or t h a t o f t h e m o n o c h r o m a t i c g a m m a rays f r o m the Li(p, 7) reaction. a) T h e m a x i m u m p h o t o n energy in the case o f h r e m s s t r a h l u n g . b) Results using 17.5 M e V m o n o c h r o m a t i c g a m m a rays f r o m the Li(p, 7) reaction. c) F r o m c o m p a r i s o n with (p,)'0) reaction. d) Probable value o b t a i n e d f r o m s t r o n g transition (see sect. 3). e) M o s t probable value considering 19 M e V results (see sect. 3). t) Yield is n o t great b u t a certain a m o u n t to the g r o u n d state is found.

NUCLEAR SHELL EFFECTS

309

other is for odd-proton nuclei, the spectra of which converge to ER > 0, which suggests that the ground state transition is small or does not occur around E? = 24 MeV and that most transitions leave the residual nuclei in their excited states. The numerical value ER mi, to which the spectra converge cannot be determined precisely because of the low yield of the photoprotons. If we make an extrapolation of the

4---~

3\

103

f-3 I' :~ 102

I '

o

k__

"l

"~.~V!!

i I

kl

10

t l,~, I o

12

10

8

6

4

2

E R =flA l ( E ~ m a x - E t h ) - E p

(MeV)

-L----. 0

F i g . 2. T h e energy distributions of photoprotons from odd-proton nuclei irradiated by bremsstrahlung with an energy smaller than 24.0 M e ¥ . Ordinates are the same as in fig. 1. The relation between ER and Z of nuclei shown in fig. 1 does not always hold in this low-energy case. 1.29Curef.~s), 19.0 M e V . 2. ~sMn 55 ref.l~), 20.5 M e V . 3.15P 31 ref.25), 19.0 M e V . 4. 9F 19 ref.~4), 19.0 M e V .

spectra around these regions and consider the level schemes of the residual nuclei, we can determine the most suitable energy of the lowest level of these residual nuclei. We are also able to compare these 15hotoproton reactions with (p, Vo) reactions for ground state transitions. These levels are shown in table 1. In fig. 2, the energy distributions from odd-proton nuclei from bremsstrahlung

310

K. SHODA

irradiation of lower energy are compared in the same way as in fig. 1. Some evidence for ground state transitions exists in the lower energy irradiation for the odd-proton nuclei as shown in fig. 2, though they show little ground state transition for 24 MeV bremsstrahlung irradiation. Results have been obtained for some nuclei using 17.5 MeV mono-energetic gamma rays from the Li(p, 7)reaction. We can determine from such results the lowest state of the residual nuclei after a strong transition with proton emission. These results are also shown in table 1. ld i

2s~

ld:~

If 7

2p~

7-

6-

•

i

• I 5m

m

0 ..........

n

~,y,vx;~,. I0

i ,,v

I .....

20

g,v~9 30

Z

P r o t o n n u m b e r of t a r g e t nuclei

Fig. 3. The energies of the lowest level of residual nuclei. The values are obtained from table 1. The energy level schemes of the residual nuclei are shown by horizontal bars in the figure. Circles are the values of the lowest residual energy for photon absorption around 24 MeV. Crosses are the values of the lowest residual energy for photon absorption less than 20 MeV. Vertical bars show the uncertainty of the determination of residual energy. The lowest levels obtained by the above methods are indicated in fig. 3 on the level schemes of the residual nuclei. From this figure, we can draw the following conclusions. (i) There are strong ground state transitions after the absorption of photons about 24 MeV for even-proton target nuclei. (For lower photon energies, the situation does not change considering data from lower energies and inverse reactions

(p, (ii) In odd-proton target nuclei, the lowest residual level is not the ground state for strong transitions, but some excited state for the absorption of photons about 24 MeV.

NUCLEAR

SHELL EFFECTS

311

(iii) There are some differences in the energies of the above residual states among individual odd-proton target nuclei. The residual states are very much higher for pa~ and Cu than for the other nuclei for the absorption about 24 MeV photons. These nuclei have closed proton shells plus one outer proton. (iv) In the lower photon energy region (about 17-20 MeV), strong ground state transitions are induced in some odd-proton nuclei besides even-proton nuclei; for example F 19, p31 and Cu which also have closed proton shells plus one outer proton. The nuclear shell model seems to explain qualitatively the above conclusions for residual states considering particle-hole interaction for the giant resonance. Using the particle-hole interaction model for photoreactions, some calculations 5-s) have been made for doubly closed shell nuclei, for example C 12, 016 and Ca 4°. In these calculations, the photonuclear reaction is induced by the nucleon transitions into dipole states which are described by the superposition of states formed from each nucleon shell, considering the large residual energies for particle-hole interactions. Each nucleon shell state plays an important role in the dipole states. Thus, if there exists a substantial direct particle emission in the reaction, the residual state will be expected to correspond to the hole state of the shells. Mihailovi6 and Rosina applied particle-hole considerations to nuclei having closed shell plus several nucleons. Their calculation shows that the strong transitions a r e excited by two particle-hole pairs i.e. one nucleon is excited into a higher shell while the other only suffers a change of state within the same outer shell. In this case, the residual state is expected to be formed only by the particles in the same outer nucleon shell. In some cases, it will be the ground state while in others, it will be a low-lying state produced from a mode of occupation of the particles in that shell. According to the present experimental results, many transitions leave the residual nucleus in its ground state for even-proton target nuclei, but leave it in an excited state for oddproton target nuclei. This means that paired nucleons act as if there was a closed shell, though they do not fill the shell, but in the case of an odd number of particles, the valence nucleon which is the most loosely bound in the nucleus does not play an important role in the absorption of photons of about 24 MeV. If a nucleon, but not a valence nucleon, is emitted from the outer shell of the odd-proton nuclei, the residual state should be at least a two quasi-particle state which forms a low excited level. Some difference is expected for nuclei having only one nucleon outside the closed shell because the residual state will only be a ground state when the outermost nucleon is emitted. The emission of the outermost nucleon corresponds to the pygmy resonance in the low-energy region because there is no particle-hole interaction. In p31 (ref. 25)) and Cu 63 (ref. 34)), the pygmy ground state transition is not small, however this is much smaller in Na 23 (ref. is)), A127 (ref. 32)), K39 (ref. 33)) and Mn 55 (ref. w)). If a nucleon is emitted directly from an inner closed shell of odd-proton nuclei, the residual state is also expected to be a two quasi-particle state formed by one hole and

312

K.

SHODA

one particle between different shells. Such a state will be expected to be higher t h a n states formed f r o m nucleons in the same shell. These estimations are also in good agreem e n t with the fact that the residual state is left in a higher energy level for p3~ a n d C u 63 t h a n others, because the lowest residual state is expected to be in a hole state of the i n n e r closed shell for P ~ a n d C u ~ a n d in a hole state of the outer shell for other nuclei. I

I

I

I

I

I

|

I

I

I

I

|

g

/2c

I

I

x

~ 11)" oo

'

b

,r, Ar

~

0

1~0

•

'~'¢1

12

14

,

~ ' ~ l

16

18

20

'

22

P h o t o n e n e r g y (MeV)

Fig. 4. Cross sections for P~(~, p) calculated from the energy distribution assuming complete ground state transition. Closed and open circles are those from 19 MeV and 24 MeV results respectively. The dot-and-dash straight line is a fictitious constant cross section in the region less than 16.8 MeV. Curves with open triangles and crosses are cross sections calculated from the differences between 24 MeV results and 19 MeV results and between 24 MeV results and the constant ground state cross section assumed, respectively. The assumption was made of a residual state at about 7 MeV. Dashed lines are the regions where (7, np) reactions are possible.

3. Comparison of the Energy Distributions of Photoprotons M a n y structures are observed in the p h o t o p r o t o n energy distributions as shown in figs. 1 a n d 2. These structures suggest that there exist structures in p h o t o p r o t o n cross sections a n d that residual levels are n o t c o n t i n u o u s . P h o t o p r o t o n cross sections are inversely p r o p o r t i o n a l to the n u m b e r o f p h o t o n s i n the b r e m s s t r a h l u n g a n d p r o p o r t i o n a l to the yields of p r o t o n s in the energy distri-

NUCLEAR

313

SHELL EFFECTS

butions, so t h a t it can be e s t i m a t e d f r o m the energy d i s t r i b u t i o n s with a c o r r e c t i o n for these n u m b e r s . F o r example, as s h o w n in figs. 4 - 6 a n d in refs 12,13), this is corrected b y a s s u m i n g all the p r o t o n t r a n s i t i o n s leave the residual nucleus in the g r o u n d state. C o m p a r i n g these results a n d e x p e r i m e n t a l (?, p ) cross sections m e a s u r e d directly, this a s s u m p t i o n seems g o o d in e v e n - p r o t o n nuclei lighter t h a n Si 2s b u t n o t g o o d in o d d - p r o t o n nuclei a n d nuclei 13) heavier t h a n Si 2s. H o w e v e r , the residual states a r e I

i

i

i

I

i

l

l

l

l

I

l

l

15-

I

\

I

\

I

\

/

\

',

!

10-

o=

...I/A" &

,

o

5-

i

Ii4! !!!k.

,r !l Ji

?

i

0 10

'

i2

'

/4

i6

"

1'8

'

2'0

2'2

24

P h o t o n e n e r g y (Me V )

Fig. 5. Cross sections for SS2(7, p) calculated from the energy distribution assuming complete ground state transition. Closed and open circles are those from 17 MeV and 24 MeV results respectively. Crosses are the secondary cross section calculated from the differences between 24 MeV and 17 MeV results assuming the residual state at around 5 MeV. Dashed lines show the regions where (7, np) reactions are possible. The dot-dash line shows the cross sections from (p, 70) reactions 86.sT). The broken line is the (y, p) cross section obtained from the photon difference method using ZnS scintillation counters which cannot resolve the structures in the cross section because their resolution is not sufficiently good. expected to be excited levels for o d d - p r o t o n nuclei as shown in table 1. Then, if we a s s u m e t h a t all p r o t o n t r a n s i t i o n s are to these lowest excited levels for o d d - p r o t o n nuclei, we can o b t a i n cross sections f r o m the energy d i s t r i b u t i o n s in the same w a y as before. W e expect m a n y g r o u n d state t r a n s i t i o n s in the p y g m y r e s o n a n c e for p31, at least a t energies lower t h a n 19 MeV, as m e n t i o n e d above. W e c o m p a r e the two cross sections o b t a i n e d f r o m 19 a n d 24 M e V b r e m s s t r a h l u n g a s s u m i n g c o m p l e t e t r a n s i t i o n

314

K. SHODA

to the g r o u n d state. The result is shown in fig. 4. T h e first excited state o f Si a° is at 2.2 MeV, so that there is a c o m p l e t e g r o u n d state t r a n s i t i o n in the region f r o m 16.8 M e V to 19 M e V p h o t o n energy in the 19 M e V results. The 24 M e V results are in a g r e e m e n t with the 19 M e V results f r o m 17 M e V to a b o u t 19 MeV, so t h a t we can expect the g r o u n d state cross sections in the p h o t o n energy region larger t h a n 17 M e V in the 24 M e V results. T h o u g h we have no justification in d e t e r m i n i n g the g r o u n d state

tl

0 ~ 10

1

1

/

/

15

•

20

Photon energy (MeV)

Fig. 6. Cross sections for Ca 4° calculated from the energy distribution irradiated by 20.5 MeV brcmsstrahlung assuming a complete ground state transition. The result is shown by open circles. The dotdash line is a ground state transition cross section from (p, ~'0) reaction ~v). Crosses indicate the secondary cross section calculated from the differences between 20.5 MeV result and the ground state transition cross section, assuming the residual state at 2.8 McV, the corresponding scale is shown on the right hand side of the figure. t r a n s i t i o n lower t h a n 16.8 MeV, we assume two cross sections; the first c o r r e s p o n d i n g to a c o m p l e t e g r o u n d state transition for the 19 M e V results a n d the second to a constant cross section as great as that a r o u n d 16.8 MeV. F u r t h e r cross sections can be o b t a i n e d b y a s s u m i n g t h a t the strongest t r a n s i t i o n is a residual state a r o u n d 7 MeV, because the discrepancy between the a b o v e two cross sections f r o m 19 a n d 24 M e V results becomes greater for p h o t o n energies o f a b o u t 7 M e V less t h a n 24 MeV. The results are also shown in fig. 4 for these two a s s u m p t i o n s for the g r o u n d state transition. F o r S 32, (y, Po) cross sections can be o b t a i n e d for the g r o u n d state transition f r o m (P, 70) results 36, 37) a n d also f r o m energy distributions f r o m i r r a d i a t i o n b y 17 a n d

NUCLEAR

SHELL EFFECTS

315

24 MeV bremsstrahlung (assuming complete ground state transitions). The cross sections from 24 MeV irradiation are very different to those for the ground state transition from (p, 70) and 17 MeV results in the photon energy region lower than 17 MeV. The secondary cross section can be obtained by subtraction of the 17 MeV results from the 24 MeV results t assuming the resultant spectrum is to the excited residual state around 5 MeV. The result is shown in fig. 5. The same method is applied to the Ca 4° case. The secondary cross section is shown in fig. 6 assuming a residual state of 2.8 MeV. The energy of 2.8 MeV corresponds to the difference of binding energies of ld~ and 2s~r from (p, 2p) reactions 38). It will be reasonable to assume that the secondary cross section can be attributed to the emission of a 2s÷ proton. As mentioned in sect. 2, if we assume that the paired nucleons play an important role in the outer shell, we can expect some similarities in t h e energy distributions between Z = 2n and Z = 2n + 1 nuclei. In figs. 7 and 8, the cross sections are compared assuming a complete ground state transition for even-proton nuclei and a complete excited state transition for odd-proton nuclei. The results from the complete ground state transition of S 32 shown in fig. 8 are very different from those of nuclei lighter than p31, however the secondary cross section from transitions to a 5 MeV residual level agrees with the other lighter nuclei as shown in fig. 7. We can expect these cross sections to come from the same shell effect. A tail in the proton distribution for N a z3 is observed which indicates the existence o f a transition to the state of 1.27 MeV considering the maximum energy of the energy distribution. But a much stonger transition can be expected to the 3.35 MeV level because a great many protons are raised corresponding to this level, and the cross sections calculated from the energy distribution assuming this last residual energy fits better to that of Ne 2° as shown in fig. 7. In the case of K 39 and Ca 4°, they are similar for energies lower than 17 MeV but some discrepancies are observed in the region higher than 17 MeV. The results for Ca 4° are obtained from 20.5 MeV irradiation, while the K 39 results are from 24 MeV irradiation. Therefore, some differences in their energy distributions would be expected, because of the different energies of photons absorbed. In fact, the energy distributions 41) from C a 40, irradiated by bremsstrahlung of a higher energy (85 MeV), is in agreement with the K 39 results. The shape of the cross section assuming complete ground or excited state transition is very different between groups of nuclei occupying the d~ shell (fig. 7), the s~r shell (S 32 in fig. 8), the d~ shell (K a9 and Ca 4° in fig. 8) and the f~ shell (Fe 56 in fig. 8). t The difference in the cross sections around 15.5 MeV for the ground state transition is significant between the 17 MeV bremsstrahlung experiment 37) and the (p,)'0) experiment 37) as shown in fig. 5. This difference is interpreted by considering that since the peaks found in (p,)'0) result are very sharp and of small width, they do not contribute much to the integrated cross section in that region. Then the peaks may not be apparent in the 17 MeV results because the resolution for the emulsion experiment is poorer l~han in the (p,)'o) experiment.

316

K. SHODA

T h i s is e v i d e n c e f o r n u c l e a r s h e l l d e p e n d e n c e s f o r p h o t o n u c l e a r

r e a c t i o n s . A n d it is

i n t e r e s t i n g t o d r a w a t t e n t i o n t o t h e f a c t t h a t t h e r e s u l t s o f p31 a r e i n c l o s e r a g r e e m e n t t o t h e d~ s h e l l g r o u p t h a n t h e r e s u l t s f r o m t h e g r o u n d s t a t e t r a n s i t i o n o f S 32, e v e n t h o u g h t h e y h a v e o n e a n d t w o p r o t o n s i n t h e 2s~ shell, r e s p e c t i v e l y . T h i s s u g g e s t s ,

,

I

I

[

l

l

i

l

l

l

l

10-

Z

==

<

0

5

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b.

.o L)

--/ /

','

/

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i

-10

I

/ 0

5 '

1'5

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~'~

Photon energy (MeV)

Fig. 7, Comparison of the cross sections of 1d-2s shell nuclei calculated from the photoproton energy distributions assuming complete ground state transition for even-proton nuclei and excited state for odd-proton nuclei. The energy of the excited state is used as shown in table 1. For Na sa, the residual energy was determined for strong transition which is the best fit between the results of Ne 2° and N a 2a. For Sa2, the secondary cross sections, assuming the residual state at around 5 MeV, are compared with the ~ nuclei, and the dotted line represents the same spectrum shifted a little to obtain the best fit. Dashed lines shows the regions where (7, np) reactions are possible. 1. S a2 refs. is, ~s) (residual energy = 5 MeV) 2. p31 refs. 14, ~5). 3. Si ~s ref. 14). 4. Mg ~4 reL 2~). 5. A1z7 ref. 19). 6. Na aa re/'. xs). 7. Ne z° ref. 8~).

NUCLEAR SHELL EFFECTS

3 17

that one valence nucleon in the 2s{r shell o f pal has no great effect on the giant resonance as shown in sect. 2. The assumption that photoproton transitions leave only one state in the residual nuclei seems more valid in the nuclei lighter than pa, but ,

i

,

i

I

i

,

i

,

l

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i

,

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,'N

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l

15

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i

20 Photon energy (MeV)

'

~

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0

25

Fig. 8. Comparison of the cross sections of nuclei heavier than Sa~ assuming complete ground state transition for even-proton nuclei and excited state transition for odd-proton nuclei. The secondary cross section for Ca4° is also compared with the results for S32. The dotted line is a secondary cross section of Ca4° shifted l MeV to obtain a best fit to the S8~ result. The broken lines show the regions where (~, np) reactions are possible. 1. C a 4° r e L ~ )

(residual

energy

~ 2.8 M e V ) 2. S 3~ ref.16). 3. F e 66 ref.l~). 4. K a9 ref.~°). 5. C a 4° ref.~5).

not so valid in the heavier nuclei. In the latter case, a few additional strong transitions to excited states must be added. The secondary transition cross section o f S az to the residual energy of 5 MeV agrees with those o f the ld~ shell nuclei as mentioned before. Thus, it can be considered that this secondary group is from the ld~ core. Similarly, we compare the

318

K. SHODA

secondary cross section of Ca 4° for a transition to the residual state of 2.8 MeV with that from ground state transition of S 32. The comparison is shown in fig. 8. Fairly good agreement is found in both cross sections especially if one is shifted about 1 MeV. These cross sections can be considered to result from transitions from closed shells within the 2s~ shell. These cross sections may also be divided into two main contributions at 16.5 MeV for S 32 as shown in fig. 5, corresponding to 2s~ and ld~ proton transitions. The corresponding energy to this boundary is about 14.5 MeV for the cross section of Ca 4° assuming the ground state transition, which shows the residual state to be about 6 MeV. This energy also agrees with the difference in binding energies of ld~ (15.0 MeV) and ld~ (8.6 MeV) protons in the (p, 2p) experiment 38). This conclusion is the same as that of Johansson et al. 28). 4. Comparison of the Angular Distributions of Photoprotons

Angular distributions are expected to be of the form a + b sin 2 0 for dipole transitions. The value b/a can be determined using a least-squares fit to the available data. The results are shown in fig. 9 as a function of excitation energy assuming ground state transitions and the excited state transitions mentioned in sect. 3. Those for excited state transitions of pax and S 32 are obtained by subtraction of the 19 MeV data 25) for p3~ and the 17 MeV data 27) for S 32 from the 24 MeV results and are shown on the left hand side of the figure. On the right hand side of the figure, the angular distributions in the region of the secondary cross section of Ca 4° is compared with the S 32 and Fe 56 results. For Ne 2°, A127, Si 2a, pal and the secondary excited parts of S 32, b/a shows a similar tendency except for the lower energy part of Ne 2°. In Ca 4°, b/a for the secondary excited transition also shows a similar tendency to that of the ground state transition in S a2, but different from the Fe 56 results. Such similar tendencies cannot be expected without the assumption of the transition to the residual state energy mentioned above. According to Courant's calculations 2), the angular distributions of photoprotons are do" - - oc l+½(I+2) sin 2 0 for the l ~ 1+1 transition, dI2 do"

- - oc l + ½ ( l - 1 ) sin20 for the 1 ~ l--1 transition, dr2 where I is the orbital angular momentum carried by the emitted proton within the nucleus. Wilkinson 4) predicted that only the l ~ l + 1 transitions should be important for the point of view of the shell model. We expect the value of b/a from this model to be oo (a = 0) from the s orbital proton, 1.5 from the p orbital proton, 1 from the d orbital proton and 0.83 from the f orbital proton. As shown in fig. 9, the

NUCLEAR SHELL EFFECTS

319

value of b/a is close to 1 for Ne 2°, A127, Si 28, paa and the secondary transition of S 32 for a photon energy around 20 MeV; larger than 2 for S a2 and the secondary transition from Ca 4° around 19 MeV and less than 1 for Fe 56 around 20 MeV. They are not contradictory to d, s and f state proton emission as expected from the shell

4-

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Ne20 39)40)

1"

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o

3o

$32 16)

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0.

I

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i

I

11 A127 19)

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i

i

)

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8i28 14) 2.m 0-

i

Ca40 25) (residual energy = 2.8 MeV)

i---7--

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i

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)

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1~ S32 16)28) ~ (residual energy = 5 MeV) 011 I ' '

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20

i

' 11~ 22 Photon energy (MeV)

1'6

118

'210

Fig. 9. Angular distributions of the photoprotons. The photon energy is determined as in figs. 7 and 8. T h e angular distributions in the left column correspond to the energy distributions in fig. 7. T h o s e in the right column correspond to fig. 8. Open circles in N e z° are obtained from the (e, e'p) reactions in ref. 40). The broken crosses are from ref. 2s).

model. However, for the low-energy side, the values are much reduced and sometimes negative with exception of Ne 2°. These reductions are considered to be the result o f mixing other additional processes; for example, compound processes of M I transitions e t c . . . These additional processes lead to excessive yields for the lower energy

320

K. SHODA

side of the spectra in figs. 7 and 8. The rise of the value of b/a for the lower energy side of Ne 2° may be expected from the large dependence on the p orbital proton. For S 32 and the secondary cross section of Ca 4°, the spectra seem to be separated into two parts at a photon energy of about 16.5 MeV as shown in sect. 3. Protons from s and d orbits were expected for the high and low energy parts of the energy distribution, respectively. This also does not contradict the experimental angular distribution. The experimental data are not precise enough at present to determine the mechanism of photoproton emission, however they do not show any serious contradiction with the direct emission model in the region of the giant resonance. More precise measurements are required to study this in more detail. 5. Discussion

It was found that the main residual state was the ground state for even-proton nuclei and an excited state for odd-proton nuclei. When the residual energy was assumed as in table 1, the cross sections were calculated assuming the main strong transition to these levels. For nuclei from Ne 2° to p3~ and the secondary transitions for S 32, the shapes of cross sections and angular distributions were similar. If such excited states were not assumed, the cross sections and angular distributions were greatly shifted with respect to each other. This situation seemed to be the same for nuclei heavier than S 32, although the secondary cross sections became much larger. Considering the experimental results for heavy nuclei 42), such relations between the residual level and the proton number Z seem to hold for the nuclei heavier than Zn which are not discussed in this paper. All the evidence suggests that the reactions are due to direct emission from paired protons in the outer shell and secondary inner shells. We have not considered the correlation between protons and neutrons in the nucleus. The available photoneutron energy distributions 4.3--46) can be compared with the photoproton results for A127, Si 2s, S32, Ca 4° besides C 12 and 016, although the irradiation energies are somewhat different. The comparison between photoneutron energy distributions and (p, ~o) reaction cross sections shows good agreement in their fine structure although additional structure is found in the photoneutron case 43). This agreement shows the formation of the compound levels after absorption of photons. Many peaks in the fine structure seem to make several gross peaks together which show the gross mechanism of the reaction that we have discussed. Photoneutron experiments are usually performed with natural nuclei which contain mainly even-neutron nuclei. Therefore it is expected that the ground state transition is very large in comparison with the photoproton case, and this expectation agrees with the experimental results in the maximum energy region of the available energy distributions of photoneutrons. In id-2s shell nuclei, odd-proton nuclei usually have the same numbers of neutrons

321

NUCLEAR SHELL EFFECTS

as protons and as the neutrons in Z + 1 nuclei for the m o s t a b u n d a n t isotope. Therefore, the p h o t o n e u t r o n energy distributions should be almost the same as in both neighbouring nuclei although there exist differences in the energy distributions o f p h o t o p r o t o n s between them in the energy o f the residual states. Some cross sections ,

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F i g . 10. C o m p a r i s o n

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20 Photon energy (MeV)

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25

b e t w e e n (7, n ) a n d (7, P ) r e a c t i o n s f o r A1 ~ . S o l i d l i n e s a r e c r o s s s e c t i o n s

calculated from the energy distributions for (7, n) (ref. 45)) and (~, p) assuming complete ground and excited state transition respectively. The broken line is the 0', n) cross section from the photon difference method ~0. are c o m p a r e d in figs. 10-12, for p h o t o n e u t r o n cross sections obtained by the p h o t o n difference method, and those calculated by the energy distributions o f photoneutrons, assuming complete g r o u n d state transitions t for A127, Si 2s, S 32 and those o f (7, P) discussed previously. A structure o f three large peaks is f o u n d in the cross sections o f A127 and Si 2s which is nearly the same in b o t h nuclei except for its energy, while that o f S 32 is different. The cross sections f r o m the energy distributions have a structure * A continuous evaporation process is assumed and subtracted from the energy distributions in the original paper for AlZT(7,p). However, a complete ground state transition is assumed in fig. 10 for comparison with the other results.

322

K. SHODA

corresponding to these peaks. The third large peak in the cross sections o f A127 and Si 2s does not correspond to large peaks in the cross section from energy distributions. This peak may be considered to be due to some contribution from the inner shell which left the residual nuclei in a highly excited state. The (Y, n) process does not seem I

~

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Photon energy (MeV)

Fig. 11. Comparison between (7, n) and (~, p) reactions for Si2s. Solid lines are the cross sections calculated from the energy distributions for (~', n) (ref. 44)) and (y, p) assuming complete ground state transitions. The broken line is the (7, n) cross section from neutron counting using monochromatic annihilation gamma rays 48). to be very different for A127 and Si 28 which have the same number of neutrons. More precise measurements o f AI data are required for a more complete comparison. Another clearer comparison is suggested for the experiments on P31(7, n). The pa~ nucleus has a closed ld÷ shell plus one 2s~ proton and two 2s~ neutrons. It is very interesting to compare the energy and angular distributions of (7, n) and (7, P) for p31 and S az. If the correlations between the proton and neutron are not very strong, the results o f (7, n) from p3t must not be very different from those of(?, n) and (7, P) from S 32 shown in fig. 12, because they have the same shell contribution for the neu-

NUCLEAR

323

SHELL EFFECTS

tron in both nuclei and for the protons in S 32. I f the correlations are very strong, the results of p31(?, n) must correspond to the (% p) result of p31 which shows a marked difference for energy distribution from S 32. We have not considered the A 4° results. The energy distributions do not agree with each other 40, so, sl). However, the results from a precise measurement using an analysing magnet 40) seem to resemble those of K39(]), p)20) and Ca*°(?, p) l

i

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~(~,~/ [

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-

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20 MeV)

Fig. 12. Comparison between (Y, n) and (7, P) reactions for Sa2. Solid lines are the cross sections calculated from the energy distributions for (7, n) (ref. 43)) and 0', P) assuming complete ground state transitions. The broken line is the (y, n) cross section from the photon difference method 49). irradiated by 85 MeV bremsstrahlung 4a). Unfortunately, the high-energy side of the energy distribution is not certain. I f a comparison were made between the energy distributions of (7, P) and (7, n) from A 4°, it would give another way of examining the correlation between proton and neutron, because A 4° has two ld~ protons and two lf~ neutrons out of the closed shells of 2s~_and ld~, respectively. I f the correlation is not strong, the result of (~, p) will show a marked difference from that of (?, n). The residual states can be compared with those from other reactions if we assume the production of a hole state in the residual states for the direct process. As an example, deuteron spectra observed by the (n, d) reaction using 14 MeV neutrons might

324

K. SHODA

correspond to residual levels of a proton hole state if a proton is picked up directly, though the direct transition and hole state have never been confirmed. The results o f AlZT(n, d) show m a n y residual levels 52, 5a), and the 3.6 M e V level is possibly a hole state o f ld~ orbit 53), which agrees with the (y, p) result. N o large peaks exist in P31(n, d) corresponding to residual levels less than 5 M e V except the g r o u n d state 54). I n $32(n, d) there seems to exist some small levels less than 4 M e V o f residual energy but they are not certain and not large 54). These do n o t contradict our conclusions that the hole-states m a y be 7 M e V and a b o u t 5 M e V for pal(y, p) and $32(V, p) respectively. I n Ca4°(n, d), peaks are f o u n d corresponding to the g r o u n d state, 2.8 M e V and higher than 4 M e V o f residual energy 52). The 2.8 M e V level corresponds to 2s~r hole-state f r o m Ca4°(V, p). The results do not seem contradictory either for Mn55(n, d), C059(n, d), Mn55(y, p) and coSg(y, p). It seems that no large peaks exist corresponding to residual states for Cu63(n, d) between the g r o u n d state and the 4.5 M e V state 52) which also agrees well with the (y, p) result. These comparisons between (n, d) and (y, p) reactions show g o o d agreement for residual states. It m a y be p r o o f o f a hole-state although evidence has n o t yet been f o u n d directly in (n, d) reactions.

The author wishes to acknowledge the support of the Ministry of Education of Japan which made his stay at Orsay possible, and to thank Professor A. BlancLapierre for his hospitality during his stay. He also thanks Professor G. R. Bishop for reading the manuscript. References 1) M. Goldhaber and E. Teller, Phys. Rev. 74 (1948) 1046; H. Steinwedel and J. H. D. Jensen, Z. Naturf. 5a 0950) 413 2) E. D. Courant, Phys. Rev. 82 (1951) 703 3) J. L. Burkhardt, Phys. Rev. 91 (1953) 420 4) D. H. Wilkinson, Physica 22 (1956) 1039 5) G. E. Brown and M. Bolsterli, Phys. Rev. Lett. 3 (1959) 472 6) N. Vinh-Mau and G. E. Brown, Nuclear Physics 29 (1962) 89 7) G. E. Brown, L. Castillejo and J. A. Evans, Nuclear Physics 22 0961) 1 8) V. Gillet and N. Vinh-Mau, Phys. Lett. 1 (1962) 25 9) B. R. Easlea, Phys. Lett. 1 0962) 163 10) M.V. Mihailovi6 and M. Rosina, Nuclear Physics 40 (1963) 252 11) S. A. E. Johansson and B. Forkman, Ark. Fys. 12 (1957) 359; C. Milone et al., Nuovo Cim. 7 (1958) 729; J. P. Elliott and B. H. Flowers, Proc. Roy. Soc. A242 (1957) 57 12) E. Hayward, Revs. Mod. Phys. 35 (1963) 324 13) K. Shoda et al., J. Phys. Soc. Japan 17 (1962) 735 14) K. Shoda et al., J. Phys. Soc. Japan 16 (1961) 1807 15) M. E. Toms and W. E. Stephens, Phys. Key. 82 (1951) 709 16) K. Shoda et al., J. Phys. Soc. Japan 18 (1963) 152 17) K. Shoda et al., to be published 18) K. Shoda et al., to be published 19) K. Shoda e t a L , J. Phys. Soc. Japan 17 (1962) 1535 20) K. Shoda et al., J. Phys. Soc. Japan 17 (1962) 1083

NUCLEAR SHELL EFFECTS

21) 22) 23) 24) 25) 26) 27) 28) 29) 30) 31) 32) 33) 34) 35) 36) 37) 38) 39) 40) 41) 42) 43) 44) 45) 46) 47) 48) 49) 50) 51) 52) 53) 54) 55)

325

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