Nuclear structure studies with high energy heavy ions

NUCLEAR

INSTRUMENTS

AND

METHODS

2 8 (I964)

I6O-I79; © NORTH-HOLLAND

PUBLISHING

CO.

NUCLEAR STRUCTURE STUDIES WITH HIGH ENERGY HEAVY IONS* D. A. BROMLEY Yale University, New Haven, Connecticut

With improved instrumentationit has become possible to examine a variety of otherwise inaccessible nuclear phenomena utilizing high energy beams from the Yale Heavy Ion Accelerator. Selected examples will be presented illustrating a number of the unique features of these high energy reactions and emphasizing the nuclear structure potential of the heavy ion beams from the Emperor accelerators. In Li6 induced interactions it has been demonstrated that dissociation of the projectile dominates at higher energies; characteristics of the dissociation mechanism have been studied supporting a pronounced binary cluster structure. Deuteron and nucleon transfer reactions to isolated final nuclear states have been examined; at high energies these show promise of providing a direct probe for determination of frac-

tional parentage information, and of the location and character of two-particle states in nuclei. It has been demonstrated that inelastic scattering of heavy ions preferentially excites collective nuclear states; the deformations indicated by DWBA analyses of the inelastic scattering data are in reasonable accord with those obtained from electrcmagrelic studies. Multiple coulomb excitation measurements wiih O 16 ions have ir,cluded studies of interband mixing in even-even nuclei a~d of higher order Coriolis perturbations in odd A nuclei, in the rare earlh region. In the former it has been demonstrated that mixing of the ground state and beta vibrational bands is dominant; in the latter, that third order perturbation effects are required to fit the higher excitations in the rotational bands.

1. Introduction

cases.

Following installation of a magnetic b e a m analysis system, a n d heavily shielded cave facilities for use with the Yale H I L A C i ) , as shown schematically in fig. l, it has been possible to overcome these limitations in part. Experience and i n s t r u m e n t a t i o n developed in this work with relatively high energy heavy ion beams ( ~< 10 M e W nucleon) is of direct relevance to our p l a n n e d p r o g r a m for the Yale M P - I E m p e r o r t a n d e m accelerator 2) which will provide a n unparalleled source of precisely controlled heavy ion beams. I n the time available I shall somewhat arbitrarily

* Work supported in part by the U.S. Atomic Energy Commission.

1) E. L° Hubbard et al., RSI 32 (1961) 621. 2) D. A. Bromley, Nucleonics 21 (1963) 48.

With improved techniques and, in particular, better energy resolution it has become clear that heavy ion induced nuclear interactions offer a n u m b e r of unique advantages in the study of nuclear structure. Such measurements with E N t a n d e m Van de Graaff accelerators have already been extremely productive b u t have been limited by the m a x i m u m energies available; those with the higher energy H I L A C beams have been limited by the attainable energy resolution or duty cycle, in m a n y

Tar et

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BEAM SWITCH YARD

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Terminal Klystron sources buniher

iO,sch r e co,utah Quadrupole lens

C - Cockroft-Walton injector, 750 kV

Area no. 4

Fig. 1. Schematic diagram of the Yale Heavy Ion Linear Accelerator. 160

N U C L E A R S T R U C T U R E STUDIES W I T H HIGH ENERGY HEAVY IONS

select four areas of recent research in our laboratory which illustrate a number of the specific advantages of nuclear studies with high energy heavy ions and the relevant instrumentation which has been evolved. The scattering studies have been carried out by A. M. Smith, J. C. Hiebert and G. T. Garvey, the dissociation and transfer studies by R. W. Ollerhead, M. W. Sachs, C. Chasman and D. A. Bromley and the Coulomb excitation studies by J. S. Greenberg, G. C. Seaman, E. V. Bishop and D. A. Bromley.

2. Isotope identification One of the major problems in high energy heavy ion studies concerns the plethora of reaction products, reflecting the very large number of open reaction exit channels, in order to minimize this confusion we have developed a charged particle identification telescope utilizing the well known d E / d x - E technique. This is based on the Bethe-Bloch equation for the energy loss of charged particles of mass M, charge Z e and energy E traversing matter: dx =

rnv z

~ KMZ2/E

(2)

Here primes denote the stopping material; I is a mean ionization energy and m is the electron mass. In eq. (2),

Fig. 2. Direct oscillographic plot of AE vs. E pulse heights from reaction productsfrom 147 MeV N 14bombardment of aluminum.

161

K is an approximate instrumental constant over a wide range of energy E; to the extent that it may be considered constant it is clear from eq. (2) that a plot of d E / d x versus E, as determined by a transmission and residual energy detector respectively, would be expected to be hyperbolic with each hyperbolic locus characterized by the M Z 2 product. Previous systems 3) have readily provided elemental separation represented by adjacent Z values; the present system4), to our knowledge, is the first which has successfully provided isotopic separation (i.e. adjacent M values) for Z > 2 and does so for Z~<9. Fig. 2 shows a direct oscillographic plot corresponding to 147MeV nitrogen bombardment of aluminum obtained using a special ionization chamber transmission detector s) and a thick, phosphorus-diffused, residual energy detector. Oxygen and higher Z products are suppressed here through limiting of the A E amplifier output but the nitrogen, carbon, boron, beryllium, lithium and helium loci are clearly evident with the fold-back of the latter reflecting inadequate thickness of the particular semiconductor detector in use to stop the higher energy alpha particles and lithium ions. Prior to the acquisition of a 20 000 channel multiparameter analyzer 6) for use with this system, advantage was taken of the fact that the product of the A E and E signals, assuming constant K, uniquely identifies each species (M, Z). Using an analog multiplier the plot of multiplier output versus energy, for 126 MeV carbon on carbon, and the corresponding multiplier output spectrum are shown in fig. 3. By setting voltage gates on selected peaks in this spectrum it has been possible to examine the energy spectra of up to 8 species simultaneously by routing appropriate pulses to one of 8-100 channel analyzer memory blocks. With the availability of the 20 000 channel analyzer the multiplier becomes unnecessary except in moie complex experiments; fig. 4 presents a corresponding photograph of a section of the analyzer display in a study of the O 16 and A127 interaction. Separation of the O ~7, O ~6 and 015 loci is clearly evident here; extraction 3) j. Schintlemeister, Physik. Z. 39 (1938) 612. B. Wolfe, A. Siverman and J. W. DeWire, RSI 26 (1955) 504. F. A. Aschenbrenner, Phys. Rev. 98 (1955) 657. 4) D. A. Bromley, N. Sachs and C. E. Anderson, Proc. of Harwell Conf. on Nuclear Instrumentation, ed. by J. B. Birks, (Heywood and Sons, London 1962) C. E. Anderson, D. A. Bromley and M. Sachs, Nucl. Instr. and Meth. 13 (1961) 238. 5) C. Chasman, J. Allen, M. Sachs, J. Poth and D. A. Bromley, Nucl. Instr. and Meth., (to be published). 6) Manufactured to joint Y a l e - - O R N L specifications by the Tullamore Division of Victoreen Instruments, Chicago, Illinois. VI. E X P E R I M E N T A L T E C H N I Q U E S

162

D.A. BROMLEY

Illustrations of the use of this system will be presented in connection with the first three research examples to follow.

3. Inelastic scattering Only very few studies on inelastic scattering of heavy ions have been reported, as yet, reflecting the general unavailability of adequate beam energies and energy resolution to make such studies possible. Those which have been reported have confirmed the expectation that inelastic scattering of heavy ions provides a unique probe for excitation and study of collective behaviour in the nuclei involved. This reflects the fact that, for a given energy delivered to the reacting system, the heavy

1 0 ¢1

o~ O

E(dE/dx) multiplier output 126 MeV C 12 ions on C 12 i

i

r

i

E

,

i

|J" !.2"

t

,

C12

22 20 18

' 'He 3 ~He4 , / / Li6

16 ; , 14 >~ 12 10

Multiplier spectrum C12+C 12 126.5 MeV £1ab 17°

t LiT

, 20

,L__,£jLz 40 60

I

•

'

,' I]"

8

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•

.

B 10 Be7

l'tlt I Itll

'/Bll

. . . .

80

.¢ ~ ~ . . . . . 100

J 120

140

, 160

Channel number Fig. 3. Direct oscillographic plot of multiplier output vs. E pulse heights f r o m reaction products from 126 MeV C 12 b o m b a r d m e n t on carbon and corresponding multiplier spectrum.

of spectral data is performed automatically by transferring the magnetic tape from the analyzer directly to the 709 computer. We are currently utilizing comp programs which fit the hyperbolic isotopic loci and extract energy spectra for individual species therefromV). In our MP-1 laboratory we shall connect this analyzer directly to a SDS-930 on-line computer and are currently planning to provide, in addition, the interface hardware linking the SDS-930 to our Computer Center IBM 7094 for priority interrupt treatment of programs and data blocks transcending the memory capabilities of the local computer.

"."

.,. ,,.:~.,,.r, ':;;'!'

Fig. 4. Section of 20000 channel multiparameter display f r o m 168 MeV O a0 ion b o m b a r d m e n t of aluminum. Three oxygen, two nitrogen, two carbon and two boron loci are clearly separated.

ion carries relatively high angular momentum and, more important, because of its short mean free path in nuclear matter, interacts preferentially via surface ,nodes. Several characteristic differences do exist in the heavy ion studies. Because the incident ion normally has low lying excited states, as compared to hydrogen or helium projectiles, simultaneous excitation of both target and 7) This p r o g r a m has been developed and written by Mr. Joel B i r n b a u m of this laboratory.

NUCLEAR STRUCTURE STUDIES W I T H HIGH ENERGY HEAVY IONS

projectile must be considered. While Pinkston and Satchler a) have demonstrated that, in inelastic nucleon scattering at high energy, coherent summation of the direct nucleon-nucleon interactions throughout the target volume results in precisely the same collective enhancement of the inelastic scattering and electromagnetic transition matrix elements, linking the same two states, the same conclusion need not apply to the heavy ion scattering where the evaluation of the matrix element is restricted to the nuclear surfaces. Hiebert

~-'~" ,~ I00 I' , 11

el

"~\

163

016 ~ C 12 elas'tic s e £ t t e r i n g = E c m = 72.0 MeV

\\

•

llI,

,

'

I0001 CARBON mSPECTRUM C'z+C 'z

=~1

Q:-4.4] ~

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°°

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15

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irl

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!

i

I !

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40

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45

016 ~ C 12 inelastic sc at t e r i n g Q = -6.14 MeV E c ' m ' = 7 2 " 0 MeV

100

(MeV)

!

40

r

k

1

~0 30 40 50 EO 70 eO ENERGY DEPOSITED IN SEMICONDUCTORDETECTOR

k "I

016 -~C 12 i n ; l a s t i ; sea tte'ri~g--i Q = -4.43 MeV ! Ec rn = 72.0 MeV i

.....

! "!11 ITENTATIVEI

I

20

"~ II1

126.5 M e V

IO

15

~IF ]

i'

~--

,

t

/ 1 t

Fig. 5. Energy spectrum of C 12 ions from 126 MeV C 12 bombardment of a carbon target.

and Garvey 9'~°) have investigated this question in some detail as will be discussed below. Fig. 5 presents a typical spectrum of C ~2 nuclei inelastically scattered by a carbon target when bombarded with 126 MeV C ~2 ions as obtained with the previously described particle identification system~). This spectrum provides striking evidence for the selectivity of the inelastic scattering reaction in popus) G. T. Pinkston and G. R. Satchler, Proc. of Kingston Conf., ed. by D. A. Bromley and E. W. Vogt, (Univ. of Toronto Press, 1960) 394. 9) j. C. Hiebert and G. T. Garvey, Phys. Rev., (to be published). t0) j. C. Hiebert, Doctoral Dissertation, Yale University, (un-

published) 1963. 11) C. Chasman and D. A. Bromley, Bull. Am. Phys. Soc. Ser. I1, I (1962) 36. 12) G. T. Garvey, A. M. Smith and J. C. Hiebert, Phys. Rev. 1311 (1963) 2397. ]3) A. M. Smith, Doctoral Dissertation, Yale University, (unpublished) 1962.

.

:~:

15

IF

~

ij

L m

~

I Ir

I

~

k

i I I

II

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20

IL__ I

£.

:

~l_~

25 30 35 Gc.m. (deg)

i

40

!,1

l

t

*

, I ]

45

Fig. 6. Angular distributions of of elastic and inelastically scattered oxygen ions from 168 MeV 0]6 ion bombardment of carbon.

lating residual states. As indicated, the 2 + level at 4.43 is strongly populated; the anomalously broad peak labelled as Q = - 8 . 8 6 and - 9 . 6 3 MeV was shown by Garvey, Smith and Hiebert 12'~3) to result from superposition of an electric octupole excitation of the 3- state at 9.63 and an even stronger mutual or simultaneous excitation of both carbon nuclei to their 2 + states. These authors 12"~3) used a standard twin VI. EXPERIMENTAL TECHNIQUES

164

D.A.

BROMLEY

counter, kinematic coincidence technique to isolate these excitations unambiguously. By t a k i n g a d v a n t a g e o f the zero spin c h a r a c t e r o f all reactants in the C~/(C12,C12')ClZ*(He4)Be 8 system, G a r v e y 1 4 - 1 6 ) succeeded in confirming the 3 - assignment to the 9.63 M e V state a n d establishing a 4 + assignment to the 14.09 M e V state t h r o u g h study o f the a n g u l a r distribution o f decay a l p h a particles relative to the m o m e n t u m o f the recoiling excited C 12 p a r e n t nucleus. As n o t e d in fig. 5 this latter assignment is consistent with assignment o f the 4 + state as the second m e m b e r o f a g r o u n d state r o t a t i o n a l b a n d characteristic o f a large static ( p r e s u m a b l e oblate) d e f o r m a t i o n b u t clearly does not establish such structure uniquely. Garvey14,16) o b t a i n e d a surprisingly g o o d fit to the e x p e r i m e n t a l elastic, inelastic, a n d m u t u a l inelastic a n g u l a r distributions assuming a plane wave Born a p p r o x i m a t i o n a n d a q u a d r u p o l e d e f o r m a t i o n /~2 0.16. Basse117) has also o b t a i n e d an excellent fit to these same d a t a using a s t a n d a r d d i s t o r t e d wave calculation. M o r e recently Hiebert a n d G a r v e y 9'1°) have ext e n d e d these studies to the 016 + C 12 system. Fig. 6 shows typical results o b t a i n e d ; in each case the d a s h e d curve is the P W B A fit, while the solid curve is t h a t o b t a i n e d by Basse117) in a D W B A fit using W o o d Saxon optical p a r a m e t e r s as follows;

U(r) = - (Vo + iWo)" (e (~-m/" - 1) - t

(3)

Vo = 3 0 . 5 7 M e V , W 0 = 17.18MeV, a = 1.651fm, R = 5.64 fm. In all these fitting attempts, a n d in p a r t i c u l a r those involving plane waves, it was n o t e d that the fl values, representative o f the nuclear d e f o r m a t i o n s involved, d e d u c e d from inelastic scattering studies were significantly lower t h a n those o b t a i n e d from electromagnetic transition or lifetime studies on the same states; however it was clear in these light nuclei that the states which exhibited enhanced g r o u n d state electromagnetic deexcitation matrix elements were those which were strongly excited in the inelastic scattering. M c l n t y r e a n d WanglS'19), on the other h a n d in p r e l i m i n a r y studies on the inelastic scattering o f C 12 and 016 on Pb 2°8, found that although the electromagnetic * It should be noted that use of/33 notation in table 1 is not intended to imply the existence of a static octupole deformation in Ol0; rather it provides a convenient parametrization related to the more realistic vibrational model via the usual relationship /~22 = (22 + l)h~oz. (2Cz)-I where ficoz is the vibrational quantum and Cx is the surface tension parameter in the collective Hamiltonian.

deexcitation o f the 2.6 M e V state is strongly enhanced with a deexcitation matrix element o f ~ 40 single particle units, no c o r r e s p o n d i n g strong inelastic scattering was observed. This a p p a r e n t p a r a d o x was r e m o v e d by Hiebert a n d G a r v e y 9'1°) who noted that direct c o m p a r i s o n o f the transition enhancements neglects the role o f the nuclear charge in the electromagnetic transitions. This follows from the o b s e r v a t i o n t h a t in the inelastic scattering,

daz/df2 ~ fl2A~k 2,

(4)

where as in the electromagnetic transition p r o b a b i l i t y B(E,2) o¢ Z flzA

.

(5)

C o m b i n i n g eq. 4 a n d 5 a n d eliminating fiz results in

dax

--OC

dO

k2B(E, 2) A ~(4- zz,

(6)

Z2

F r o m this it follows t h a t for large Z, even a strongly enhanced B(E, 2) need not c o r r e s p o n d to an observable inelastic scattering cross section (as in Pb 2°8 for example). As an illustration o f this, it m a y also be instructive to c o m p a r e the inelastic scattering results o f H i e b e r t a n d G a r v e y 9) using 126 M e V incident c a r b o n ions on oxygen with those o f Rowe et al. z°) using 150 M e V p r o t o n s on oxygen. Defining R =

da/d~2[2 + in O163 = B(E2; O16). Z 2 d a / d O [ 2 + in C 12)

B(E2;

C 12)

Z2'

(7)

H i e b e r t and Smith 9' 1o) find R = 0.27 ___ 0.07 and R o w e et o/. 2°) find R = 0.24 _+ 0.04. Table 1", t a k e n f r o m ref. 10 illustrates typical results o b t a i n e d in inelastic scattering involving 016 a n d 012 G. T. Garvey, Doctoral Dissertation, Yale University, (unpublished) 1962. 15) G. T. Garvey, Direct interactions and nuclear reaction mechanisms, ed. by E. Clementel and C. Villi (Gordon and Breach 1963) p. 750. 16) G. T. Garvey, Phys. Rev. (to be published). 17) R. H. Bassel, G. R. Satchler and R. M. Drisko, Proc. of Asilomar Conf. on Interactions of Complex Nuclei, ed. by Ghiorso Diamond and Conzett (Univ. of California Press, 1963). is) j. A. Mclntyre and K. H. Wang, Proc. of Asilomar Conf. on Interactions of Complex Nuclei, ed. by Ghiorso Diamond and Conzett, (Univ. of California Press, 1963). 19) K. H. Wang, Doctoral Dissertation, Yale University, (unpublished) 1963. 20) D. J. Rowe, A. B. Clegg, G. L. Salmon, and P. S. Fisher, Proc. Phys. Soc. (to be published). 14)

NUCLEAR

STRUCTURE

STUDIES

WITH

HIGH

ENERGY

HEAVY IONS

165

TABLE 1

Nucleus

Excitation

C12 O16

4.43 6.92 6.14 9.63

O16 Ct2

'

2

F~(exp.)/F~,(W)

2 2 3 3

3.2 1.1 13.6 2.9

and compares these with those obtained from electromagnetic studies. The entry in the fourth column gives the transition matrix element in Weisskopf units. The fact that/3;, values extracted in the DWBA fitting are consistently lower than those from electromagnetic transition measurements may reflect neglect of coupling

0.30 ~ 0.16 0.24 0.17

[ flz(EM) [ 0.48 0.21 0.71 0.43

between the elastic and inelastic channels in specifying the distorting optical parameters used. More extensive measurements will be required to permit detailed examination of this apparent discrepancy. With the coming availability of high energy heavy ion beams of precisely controlled energy, it is already clear that inelastic scattering studies will provide extensive information on collective nuclear behaviour and in particular on the higher spin, high excitation states which are very difficult to examine otherwise. 4. Transfer reactions Extensive measurements have been reported previously on nucleon transfer reactions21), the majority of these involving relatively low energies where classical orbit considerations might be expected to have validity, and where the transfer data provide information on the behaviour of the nucleon wave function tails at large radii in the nuclei involvedZZ). Almost all of this work has utilized the fact N 13 is stable against heavy particle emission only in the ground state and can conveniently be studied through its characteristic 10 minute positron decay following production in transfer reactions of the type ( N 14, N 13) for example23). Similar, but less extensive, measurements have been reported utilizing the 110 minute positron activity F 18 produced in (F 19, F 18)

t "G

Multiplier pulse h e i g h t ~

1800~-

I

i

i

I

i

Multiplier spectrum C 12 +B 11 115.5 MeV ~lab 19.8°

1500~-

i (i°0I

I fl~(DWBA) I

Bll

The majority of this transfer work has been carried out at Yale by Mclntyre et al., at O a k Ridge by Z u c k e r et al. and at AWRE Aldermaston by Perkin et al. 2z) G. Breit and M. E. Ebel, Phys. Rev. 103 (1956) 679. G. Breit, Handbuch der Physik 41 (Springer-Verlag, Berlin

B10 Be7 Be9 Be10

!

31)1)~ ! 20

4(1

60

81)

100

120

140

160

21) See for example, Proc. First, Second and Third Confs. on Interactions between Complex Ions. 1. ed. by Zucker, Livingston and Howard, Oak Ridge National Laboratory Report, O R N L - 2 6 0 6 (1958). 2. ed. by Zucker, Halbert and Howard, John Wiley (1960). 3. ed. by Ghiorso, Diamond and Conzett, Univ. of California Press (1963).

180 2110

Channel number Fig. 7. Isotopic separation of lithium, beryllium and boron ions from 112 MeV BI1 bombardment of C 12.

1959). G. Breit, Direct interactions and nuclear reaction mechanisms ed. by E. Clemental and C. Villi (Gordon and Breach 1963) p. 48O. 23) M. L. Halbert, T. H. Handley, J. J. Pinajian, W. H. W e b b and A. Zucker, Phys. Rev. 106 (1957) 251. J. A. Mclntyre, T. L. Watts and F. C. Johes, Bull. Am. Phys. Soc. 5 (1960) 67; Phys. Rev. 119 (1960) 1331. VI. E X P E R I M E N T A L

TECHNIQUES

166

D.A. BROMLEY

transfer reactions 24) and the 4 second delayed n e u t r o n activity o f N ~7 has been utilized in studies 25) o f multinucleon transfers such as (N 14, N 17) a n d (N 15, N t 7). O b s e r v a t i o n o f the N ~3 via range measurements has p r o v i d e d i n f o r m a t i o n on the transfer p o p u l a t i o n o f a few excited states, however the attainable resolution a n d accessible excitation range has been limited. The particle identification system described previously has been utilized by Sachs et al. 20) in recent studies o f both single a n d multinucleon transfer reactions. It has the great a d v a n t a g e o f p e r m i t t i n g simultaneous studies on several such reactions while identifying the residual states involved. One o f the most surprising results o f these studies has been the extreme degree o f selectivity observed. The system which has received most c o m p l e t e study thus far is t h a t involving 112 M e V B ~~ ions incident on C 12. Fig. 7 d e m o n s t r a t e s the isotopic s e p a r a t i o n attained using the multiplier system. The upper part o f fig. 8 shows a Be t° spectrum f r o m the p r o t o n transfer reaction C~2(B 1~, B e l ° ) N 13, illus-

trating the relatively small n u m b e r o f states p o p u l a t e d by the p r o t o n transfer. F r o m this spectrum alone, it is clearly impossible to determine whether the corres p o n d i n g excitations are in N1 a or in B 1o. This a m b i g u i t y is resolved, however, by e x a m i n a t i o n o f the lower /

~o~-

'

,,I

',,,

',~

' ,r'

a

6 EXCITATrON iN N.4

SPECTRUM C ¢ 2 ( B l I B e 9 ) N 14

Be s E N E R G Y

2,o 2°° ~ , ;,,o i ~ ,20 ~° ,o

'

E B=II5.5 MeV OLAB= 8.5 °

•

A

i

i

Be* EtA ~ (MeV)

Fig. 9. Be 9 energy spectrum from a deuteron transfer reaction.

I00

I

~

'll 0

ll5

FINAL STATE EXCITATION

(MeV)

80

3e I° ENERGY S P E C T R U M C l a ( B , ' Be to ) N ~s 7- 6 0 -

Et.AB = 115.5

uJ > ~

MeV

0LAS= 9.7 ° 40

2O

70 8O--

80 EXCITATION

Be ~) E N E R G Y

e

ua 7-

60

L__

I 9O r5 io ] . i . N N 3(MeVJ

J00

?

SPECTRUM

C r~' ( B IO, B e 9 ) N I~'

24) j. L. Perkin, R. F. Coleman and D. N. Herbert, Proc. Phys.

ELAB=105 MeV

~AB:

9"9°

4c

20

TO

80

OBSERVED

PARTICLE

90 LAB

spectrum in this figure o f Be 9 f r o m the p r o t o n transfer reaction C12(Bl°,Be9)N 13. Since Be 9 is stable only in its g r o u n d state, all structure in this spectrum necessarily reflects excitations in N 13. C o m p a r i s o n o f these two spectra then permits identification o f the m o s t strongly excited states as the ;+ , 2.365 M e V and 2 +, 3.368 MeV, first excited states o f N 13 and Be 1° respectively, with w e a k e r excitation o f the N 13 g r o u n d state. Qualitatively this m a y be a d d u c e d as evidence that the first excited state o f N 13 is largely based on a simple C 12 + p configuration while the B it g r o u n d state has a significant ( B ] ° ) 2+ + p p a r e n t a g e a m p l i tude. M u c h m o r e detailed considerations would be required to extract quantitative fractional p a r e n t a g e i n f o r m a t i o n , however it might be hoped that as m o r e o f these d a t a b e c o m e available so that the technique m a y

JL j

ENERGY

(MeV)

Fig. 8. Energy spectra of Be 10and Be 9 from single proton transfer reactions.

Soc. 79 (1962) 1033. 25) G. N. Flerov, L. Pomorski, Ja. Tys and V. V. Volkov, Proc. of Harwell Conf. on Nuclear Instrumentation, ed. by J. B. Birks, (Heywood 1962) p. 242. See also : V. V. Volkov, L. Pomorski, Ja. Tys and G. N. Flerov Direct interactions and nuclear reaction mechanisms, ed. by E. Clementel and C. Villi (Gordon and Breach, 1963) p. 994. 26) M. W. Sachs, C. Chasman and D. A. Bromley, Direct interactions and nuclear reaction mechanisms, ed. by E. Clementel and C. Villi, (Gordon and Breach, 1963) 987; Proc. of Asilomar Conf. on Interactions of Complex Nuclei, ed. by Ghiorso, Diamond and Conzett (Univ. of California Press, 1963).

N U C L E A R S T R U C T U R E STUDIES W I T H H I G H ENERGY HEAVY IONS

167

TABLE 2 (d~)02 states in N 14 J

LS representation

E::

T

1.00 3G 0.895 3F + 0.447 1G 0.786 3 D - - 0 . 1 5 1 3G + 0.600 1F

9.32 12.33 11.60

0

0.670 3p __ 0.268 3F + 0.693 1D

12.31

0.384 3S --0.400 3D q- 0.748 1p

9.92

1

0

Shell model calculations (true) Configuration 1.00 d~ 2 0.267 d_~ d~ --0.964 d52 0.120 d~ d] - - 0.068 d~ 2 - - 0.431 s½

d, + O. 9 d,

10.93

0.632 3p --0.775 1S

be calibrated against known fractional parentage situations, it will provide a direct method for obtaining this spectroscopic information. Very similar results have been obtained in the present studies on the neutron transfer reaction C I 2 ( B 11, B l o ) C 1 3 . Again utilizing the unique character of Be 9 for transfer studies, fig. 9 shows the Be 9 spectrum obtained by Sachs et al. for the deuteron transfer, C12(B11,Be9)N a4 reaction. Perhaps the most striking feature of this spectrum is the appearance of two strong peaks at relatively high excitation in N 14. The fact that Harvey e t aL, 27) in a study of the ClZ(~,d) reaction, also observed highly selective population of the 9 MeV level lends credence to the assumption that both these states have marked "two-nucleon" character. Fig. 10 illustrates this schematically and is based on arguments advanced by Harvey e t al. 27 and by True28). Because of their low internal binding energies, the carrier nuclei, Be 9 or d in these cases, will be dissociated if they collide directly with the target whereas if the impact Cr2 (B II, Be9 ) N14

( z , - ~ "z

x%.,,

Ct2( a

,

d )N 14

/ ',,@J

Fig. 10. Schematic illustration of deuteron transfer reactions.

0.~916 dff2 --(].386 s~_d÷ + 0.017 s~ d~ --0.092 d~ dk + 0.054 d~ 0.135 P½2 + 0.471 s½2 --0.746 d~ O.040s{dk--O.436d~ d~ + 0.111 d~_Z 0.328 s~2 - - 0.226 p½2 __ 0.906 d} 2 --0.141 d~ 2

parameter is too large no transfer occurs. In consequence, it might be expected qualitatively that the deuteron transfer reactions would occur only in effective grazing collisions. With 10 MeV per nucleon incident ions involved in both of these reactions, grazing collisions correspond to capture of d wave nucleons so that the N Ag states formed with greatest probability might be expected to be & t h e configuration C 12 _]_(d~)2. Spin-orbit interaction in the d-shell would be expected to raise the (d~) 2 approximately 10 MeV higher in excitation than the corresponding (d~)sz configurations. Clearly the suggested (d~_)2 configuration includes all J values from 0 to 5 inclusive. Intuitively, however, based on fig. 10, it might be expected that the two captured nucleons would occupy parallel rather than anti-parallel orbits around the C 12 target case so that in an LS representation of the residual state, the G component would be expected to dominate. Table 2 shows the LS representations of the (d~)2 configurations, computed using the Sharp and Kennedy 29) conversion coefficients; together with the results of a detailed shell model calculation by True based on realistic nuclear potentials but specifically excluding all core excitations. It is tempting to identify the two B e 9 peaks in fig. 9 with the J = 5 and J = 4 states listed here as the only ones having significant G admixture. Since the upper 4 + state has a T = 1 character it would not be populated readily in the (~,d) reaction where it would involve d o u b l e / - s p i n flip; such difficulties, of course, do not 27) B. G. Harvey, J. Cerny, R. H. Pehl and E. Rivet, Nuclear Phys. 39 (1962) 160, B. G. Harvey and J. Cerny, Phys. Rev. 120 (1960) 2162. 28) W. W. True, private communication (1963). 20) W. T. Sharp and J. M. Kennedy, Chalk River Report TPI-81, unpublished (1955). VI. E X P E R I M E N T A L T E C H N I Q U E S

168

D . A . BROMLEY

a p p l y to the ( B ~ , B e 9) d e u t e r o n transfer reaction. The fact that no significant p o p u l a t i o n o f the 0 +, T = 1, 2.31 M e V state o f N ~4 is observed in the latter reaction is attributed to the presence o f strong core excitation a m p l i t u d e s in its wave function rather t h a n to any /-spin inhibition i.e. inhibition o f singlet d e u t e r o n transfer configurations as required to p o p u l a t e the p o s t u l a t e d 4 + state at 13 MeV. S u p p o r t i n g evidence for the a b o v e J assignments comes f r o m the fact that in b o t h the (~,d) z7) and (B 11, Be9)26) reactions on O ~6, the only strongly p o p u lated state is the known, (d~)2=5 state at 1.12 MeV. It should be e m p h a s i z e d however t h a t c u r r e n t l y available

•

j ,ll

•

III!

ponentially, a n d s m o o t h l y , with angle. W h e n plotted against the linear m o m e n t u m transfers involved, the d a t a coincide. C u r r e n t two-nucleon stripping f o r m a lisms 3°) are not a d e q u a t e to explain this b e h a v i o u r ; we have not yet succeeded in o b t a i n i n g any a d e q u a t e fit to the a n g u l a r distribution data, however p r e l i m i n a r y results o b t a i n e d using a direct c o r e - c o r e scattering f o r m a l i s m evolved by G r e i d e r 3~) shows some promise here as in the case o f the single nucleon transfers at high energy discussed a b o v e where the thickness o f the nuclear surface (i.e. the wave function tails), not unexpectedly, a p p e a r s to p l a y a controlling role. In o r d e r to examine this d e u t e r o n transfer system

'

, O.%il~..: |8,'"

,011,,tn,i , Fig. 11. Section of 20000 channel analyzer display from study of 147 MeV N 14 bombardment of C 12. The upper loci are from N 15, N 14 and N j3. The lower loci are from C 13, C 12 and C 11. evidence does not establish these assignments in N L4, n o r can it preclude the possibility t h a t a closely spaced g r o u p o f states are involved*. The higher energy resolution f r o m the t a n d e m accelerators will be required to resolve these ambiguities. These reactions show promise, however, o f p r o v i d i n g relatively direct i n f o r m a t i o n on the l o c a t i o n o f the i m p o r t a n t " t w o - n u c l e o n " states in nuclei. Both in the (~,d) a n d the ( B t l , B e 9 ) reactions, the a n g u l a r distributions o f the p r o d u c t particles fall ex-

more fully B i r n b a u m a n d Bromley are currently measuring Be 9 spectrum as a function o f the B 11 energy in o r d e r to determine whether, by lowering the delivered a n g u l a r m o m e n t u m , it m a y be possible to change the relative p o p u l a t i o n o f the (d~) 2 multiplet in predictable fashion. Fig. 11 is also typical o f these m o r e recent studies utilizing the 2 0 0 0 0 channel analyzer and shows a

* Note added in proof'. More recent studies by Nagatani and

30) H. C. Newins, Proc. Phys. Soc. 76 (1960) 489. N. K. Glendenning, Nucl. Phys. 29 (1962) 109. M. El. Nadi, Proc. Phys. Soc. 70 (1957) 62. 31) K. R. Greider, Phys. Rev. 114 (1959) 786; Proc. of Asilomar

Bromley in this laboratory have demonstrated that the state at ~ 13 MeV is also populated strongly in the (cq d) reaction indicating a (dk, d~)4 + assignment with T = 0 rather than that quoted herein.

Conf. on Interactions of Complex Nuclei, ed. by Ghiorso, Diamond and Conzett (Univ. of California Press 1963); Direct interactions and nuclear reaction mechanisms, ed. by E. Clementel and C. Villi (Gordon and Breach, 1963) p. 971.

169

N U C L E A R S T R U C T U R E STUDIES WITH HIGH ENERGY HEAVY IONS

section of the map display from the N 14 -+- C a2 reactions. These data provide simultaneous spectra of both products in neutron and proton transfer reactions as well as in inelastic scattering. With a wide variety of projectile species and adequate energy resolution in the incident beam we anticipate that the tandem accelerator will open up extensive areas of experimentation, using these techniques, directed toward study of more complex nuclear configurations than have hitherto received detailed study. While penetrability factors preclude direct study of unbound multi-nucleon, or cluster states at energies near threshold, particularly in cases of high angular momentum, use of complex projectiles permits the direct insertion of the cluster into such states while the remainder of the projectile serves to balance energy and momentum and in effect to deliver the cluster through the barrier which would otherwise exist. This is readily apparent, for example, in comparing the C lz + d and C 12 + B 11 reactions as probes for two nucleon states in N 14 above the deuteron binding energy at 10.26 MeV. In the case of bound cluster states the similar advantages are obvious. 5. D i s s o c i a t i o n

Multiplier pulse height Multiplier spectrum Li 6 on C 12 elab 13.1° ELi 6 3 6 M e V '

Protons

60 5O

i Deuterons 40

studies

Earlier measurements, using low energy Li 6 beams, at Chicago 3z) and at Yale33), demonstrated that the (Li6,d) and (Li6,~) reactions proceeded via a simple direct mechanism. Since such reactions appeared to provide a unique approach to the determination of deuteron and alpha particle reduced widths of interest in astrophysical and other areas, in addition to their intrinsic nuclear structure interest, Ollerhead e t al. 34' 35) initiated a series of measurements using 36 and 63 MeV ki 6 ions in the hope that, analogous to the deuteron case, use of relatively high energies would minimize distortion effects and facilitate extraction of the spectroscopic information with minimum interference assuming that preliminary studies on known systems gave confidence in the available Li 6 form factors. Fig. 12 shows typical isotopic separation obtained for hydrogenic ions and fig. 13 shows typical deuteron spectra obtained in t h e C l 2 ( L i 6 , d ) O 16 reaction. As illustrated, no deuterons were detected corresponding to population of any of the low-lying states of 016 at these incident energies ; instead the characteristic broad maximum centered on an energy corresponding to deuterons retaining their velocity in the incident Li 6 ion suggested a completely dominant dissociation mechanism in the interaction. Similar alpha particle spectra were also observed. Earlier studies using gold targets 36) suggested that

30 20

/

"

Tritons

/ 10

/

10 k. ---

o/ •

o~

~,~..

20

i

40

I

60

I

80

100

120

140

Channel number Fig. 12. Isotopic separation of hydrogenic ions.

I6(I

180

the Li 6 dissociation mechanism was a sequential one involving Coulomb excitation of particle unstable states in the Li 6 projectile followed by their decay into the observed deuterons and alpha particles37). The shaded 32) G. C. Morrison, Phys. Rev. Letters 5 (1960) 565. 33) D. A. Bromley, A. R. Quinton, L. C. Northcliffe, R. W. Ollerhead and K. Nagatani, Proc. of Rutherford Jubilee Int. Conf., ed. by J. B. Birks (Heywood, 1961) p. 597. 34) R. W. Ollerhead, C. Chasman and D. A. Bromley, Prec. of Asilomar Conf. on Interactions of Complex Nuclei, ed. by Ghiorso, Diamond and Conzett (Univ. of California Press, 1963); Direct interactions andnuelear reaction mechanisms, ed. by E. Clementel and C. Villi, (Gordon and Breach, 1963) p. 984; Phys. Rev. (to be published). 35) R. W. Ollerhead, Doctoral Dissertation, Yale University, (unpublished) 1963. 36) C. E. Anderson, Reaction between complex nuclei, ed. by Zucker, Howard and Halbert, (Wiley, 1961) p. 67. 37) R. L. Gluckstern and G. Breit, Reaction between complex nuclei, ed. by Zucker, Howard and Halbert, (Wiley, 1961) p. 77. VI. E X P E R I M E N T A L T E C H N I Q U E S

170

D.A. BROMLEY

be reflected in a group in the inelastically scattered C 12 spectrum. Fig. 14 shows typical spectra obtained using the particle identification system; it should be noted that an inelastic scattered group of Li 6 in the 2.184 MeV particle unstable state could not reach the detector before its decay hence could not be expected in the lower spectra. These spectra show clearly the elastic and inelastic scattering to the 4.43 MeV state of C ~2 but provide only an upper limit to the population of the 2.18 MeV state. Angular distributions of the elastic and inelastic scattering involving the 2 + state exhibit the well known Blair phase rule further supporting their identification. Fig. 15 compares the differential cross sections for dissociation with those for elastic and inelastic scattering; as illustrated, a sequential mechanism fails by at least two order of magnitude, to account for the dissociation. This rather paradoxical result together with the shape of the deuteron spectra of fig. 13, implied that whatever the dissociation mechanism, it could not leave the

~1 ENERGY SPECTRA L.i 6 on OLA B

Cm 13.1°

--

ELi 6 = 36 MeV

C 12 (Li6 d) 016 GROUND STATE g uJ )-,

_L 30

"~'=6° tSo "-'

I 35

I 40

i 45

I

5O

ELi 6 = 6 3 MeV

J

4o~r L

30

2o e~

,o

400

~

,g

•

",e ~ \

5 I0 15 20 25 30 35 40 45 DEUTERON LABORATORY ENERGY (MeV)

Q=O

ENERGY SPECTRA LiG-c 12 SCATTERING Ecm = 42 MeV

~ ~

300~

50

Fig. 13. Typical deuteron energy spectra f r o m 63 MeV LiO b o m b a r d m e n t o f C j2.

area in fig. 13 is the energy range which would be accessible to the deuterons in such a simple mechanism involving only the 2.184 MeV first excited state of Li 6. In the more recent studies on the EiG+ C lz interactions, however, a Coulomb excitation mechanism was found incapable of explaining either the total dissociation cross section of 270 mb, amounting to roughly 25% of the geometric cross section, or the shape of the angular distributions which dropped much more sharply with angle than such a mechanism would have predicted. This indicated that a specifically nuclear dissociation mechanism was involved, however, it was found that the cross sections showed no maximum corresponding to grazing collision as might have been anticipated qualitatively in order to permit the emerging deuteron to remain unscathed in the interaction. I n order to examine the details of a possible sequential dissociation mechanism Ollerhead et a[. 34) examined the inelastic scattering both ofEi 6 on C lz and o f C lz on Li 6 since population of a particular state in Li 6 would

teem:256 °

20O

I00~ L~ >

40

610

[

£

80

I00

~: 4

Li e I N C I D E N T

BLAB: 1 7 2 °

~ 120

140

f

30

Q = -443

20

ec.m= 2 6

2°

IO

140

150 CHANNEL

160 NUMBER

Fig. 14. Elastic and inelastic scattering spectra in the C 12 %- Li~ system.

NUCLEAR

600]--------

--

400}

/

(

i

[

q ~

i

--

I

o

~

-

-

I

" DEUTER°N PRODUCTION OLiS(CtZc'Z)Li 6

Q : O -

~

n Li ( C - , C ) L i

Q=-2.18

---

'

T

\

'

i

'I

I

WITH

HIGH

~ --~0

--

=1~ / / =

.D-a i

/

171

HEAVY IONS

(8)

= f ch*(r)chi(r)dr"f ~*(R)V(R)tPi(R)dR.

-

--]

(9)

The second integral here represents the interaction between the incident ion and the target and in the usual formalism may be written as t(K) where K is the m o m e n t u m transfer involved in the interaction. In the first integral, the bound state wave function used by Frank and G a m m e P 9) has been inserted, q~i(r) = N e -~r" r -1

(10)

c~ = (2/~E.) -~- t7-'

(11)

where

i

.....

ENERGY

t" M = J q~*(r) 7J~(R)V(R) 7Ji(R) ~i(r) dr dR

--

7

,ot-----Io'°~ 6~--

/~

STUDIES

ANGULAR DISTRIBUTIONS

~

oo ~

~

~

2oo~

STRUCTURE

"

~

x

\',\i

and a plane wave final state has been assumed l

!

q~r(r)

=

e -ih'r

.

(12)

Substituting into eq. (9) results in

M = t(K) f (

o , | l 20

25

I

30

I

i

35

40

45

t-K)

I

e-ikrNe-~"'r-" 4~zN . . . .

+ k2

dr

(13)

(14)

.

50

~)c.rn.

Fig. 15. C o m p a r i s o n o f differential cross sections for dissociation, elastic a n d inelastic scattering in the C 12 + Li6 system.

deuteron and alpha particle with small relative momentum since otherwise the dissociation deuterons and recoil carbon ions would necessarily appear at conjugate center of mass angles, with comparable differential cross sections. An attempt to account for the observed energy spectra as resulting from purely statistical, phase-space, considerations in the three-body exit channels of the dissociation reaction failed completely, on both qualitative and quantitative grounds. On the other hand a simple direct core-core interaction model similar to those developed recently by Greider 31) and by Young 3s) has been found to give an adequate representation of the experimental data. In this, the sum of the potentials operative between the target and each of the two dissociation products is approximated by an average interaction V(R) which is a function only of the radial separation R between the target (m3) and the center of mass of the incident ion (m~ + m2). Under these conditions the reaction matrix element is written as

As a simple approximation to t(K) the form given by Yavin and FarwelP °) for scattering of 40 MeV alpha particles by carbon has been used. da _ K 2 a 4 ( c o s 2 1 0 ) . dO oc I t(K) l2

j2(2KR sin 10). (2KR sin ½0) -2 (15)

Using this form for t(K) and assuming that M depends only upon the directions of motion involved, the double differential cross section becomes

d2a cc .dQ~dQo ...

[ cot½0.Jl(2KRsin½0) ]2 e + K 2 + 4k~ ~ 4klKcos(O _qb) ,

(16)

where 0 is the effective scattering angle of the alpha particle plus deuteron center of mass, ~b is the scattering angle of the deuteron, and k I is the deuteron momentum. The solid curve of fig. 16 was obtained from eq. (16) by integrating over all scattering angles 0 and has been normalized to the data at ~b.... = 30 °. As indicated, a satisfactory fit is obtained; diffraction oscillations in the 38) J. E. Y o u n g , Phys. Rev. 116 (1959) 1201. 39) R. M. F r a n k a n d J. L. G a m m e l , Phys. Rev. 93 (1954) 463. 4o) A. I. Yavin a n d G. W. Farwell, N u c l e a r Phys. 12 (1959) 1. VI. E X P E R I M E N T A L

TECHNIQUES

172

D.A.

B R O M L E Y

l

E o

/'k

.f

\

64 eV

) Ocm,

49 M e V

Fig. 16. Angular distribution of dissociation deuterons. Statistical uncertainties are within the diameter of the datum points shown. intrinsic scattering interactions are d a m p e d out in the integration over 0. R o u g h l y equivalent fits were o b t a i n e d for 36 MeV Li 6 ions on c a r b o n a n d for both Li 6 ion energies on a nickel target. Inspection o f eq. (16) indicates that the inelastically scattered c a r b o n ions associated with the dissociation a p p e a r at very small recoil angles a n d hence would not a p p e a r in fig. 15 as m e a s u r e d ; the deuterons, on the other h a n d are spread over a wide range o f angles with however a m a x i m u m cross section at ~b = 0 in a c c o r d with both the observed energy spectra and the inelastic scattering data. The success o f this simple core-core scattering m o d e l and the very large dissociation cross section provide strong evidence for a very well developed cluster structure in Li 6 and suggest that the core-core interaction which has not been found to play a significant role in deuteron stripping, for example, m a y be o f much greater i m p o r t a n c e in such reactions involving m o r e c o m p l e x projectiles. It will be o f very considerable interest to examine the c h a r a c t e r o f the Li induced reactions in spanning the intermediate energy range f r o m p e r h a p s 10 to 30 MeV. A t very low energies an essentially pure direct mechanism has been observed; at energies ~ 10 M e V M o r r i -

16 M e V •

lk

o-

o

•

~,

~

°

o

%

i

100

200

i

300 4()0 500 600 700 8()0 E n e r g y (keV) Fig. 17. Direct gamma radiation spectra from 0 .6 bombardment of a thick Sm 152 target, at the indicated incident energies.

173

N U C L E A R S T R U C T U R E STUDIES W I T H HIGH ENERGY HEAVY IONS

son 41) has found evidence for extremely complex interaction mechanisms essentially precluding extraction of spectroscopic data and suggesting that the simplicity of the reactions at lower energy may well have reflected the effectiveness of the Coulomb field in inhibiting other than relatively long range transfer type reactions. It might be hoped that at some intermediate energy below 35 MeV, where dissociation has here been shown to dominate, an interaction mechanism susceptible to spectroscopic analysis may emerge. 6. Multiple Coulomb excitations studies It has long been recognized that utilization of heavy projectiles offers particular advantages in multiple Coulomb excitation reflecting the larger nuclear charges involved. The optimum projectile energy represents a compromise between the rapidly rising excitation function for the population of higher angular momentum, higher excitation, states via the multiple Coulomb excitation process and the appearance of copious background gamma radiation associated with nuclear reactions induced by the incident ions as their energies become comparable to, or exceed, the Coulomb barriers involved. This is illustrated in fig. 17 which presents the direct LARGE APERTURE

MOSAIC~)\ /~ /ff

gamma spectra obtained in bombardment of a separated metallic Sm 152 target with oxygen ions at the indicated energies42). At low energies it is clear that only low lying states, in this case the 2 + and 4 + members of the ground state rotational band, are significantly populated; with increasing energy the cross section for population of higher collective and intrinsic excitations increase rapidly. Because the moments of inertia of the rotational bands associated with /3 and 7 vibrational motion are similar to that of the ground state, the transitions deexciting these upper bands are grouped rather closely in energy. For example, the groups of unresolved transition around 600 keV and 1000 keV correspond respectively to transitions from the beta and g a m m a vibrational states into members of the ground state band. It should be emphasized here that measurements such as those in fig. 17 are quite impossible with targets having significant oxide contaminants since radiation associated with t h e O16(O16,n},)S31,O16(O16,p),)p31 41) G. C. Morrison, Direct interactions and nuclear reaction mechanisms, ed. by E. Clementel and C. Villi (Gordon and Breach, 1963) p. 878. 42) K. Alder, A. Bohr, T. Haus, B. Mottleson and A. Winther RPM 28 (1956) 432.

GAMMA \SPECTROMETERS \\

\

8000 GET

8EA PARALLEL MOSAIC

BACKSCATTERED PARTICLES 6000

I

I

I.oo,

,:00

ol,uI

I

•

200C

n

00

O0

O•J••

~0|

•O•0•

CHANNEL NUMBER Th Band C' 6.04 Qnd 8.78MeV

Fig. 18. Annular detector mosaic for backscattered-particle gamma radiation coincidence studies. The spectrum at the right illustrates the resolution attained with 32-1 cruz semi-conductor detectors connected in parallel and exposed to a Th a-particle source. VI. E X P E R I M E N T A L T E C H N I Q U E S

D.A.

174

BROMLEY

and 016(016, 0~)8i 28 reactions completely masks the upper transitions. In this regard it is obvious that use of heavier projectiles would have important advantages, however, quite practical intensity considerations have conditioned our use of oxygen rather than the weaker neon and argon beams available from our accelerator. Beams of Pb 2°8 which will be available from the MP tandem accelerators, by supplying appropriately enriched tetra-ethyl lead to the ion source, for example, offer enormous advantages in the field because of the high charge involved and the lack of any excited states below 2.6 MeV. It would clearly be impossible to disentangle a decay scheme from direct spectra such as those shown in fig. 17 alone and these have been supplemented by a

(3-)-

(2+) . . . . . .

ENERGY

q -- -- 1526keV I I I [ I 1327key

(6+)

--1122keq

I-

@

963

"

LEVELS

IN S m mz

1397keV

r- - r I

,

3 - - -

hanced. Fig. 18 shows a particle-gamma detection system assembled by Greenberg for use at Yale; the relatively large diameter of the H I L A C beam necessitated a large beam aperture and the mosaic semiconductor detector has an area of 32 cm. An illustration of the coincidence spectra obtained will appear in a later figure. Fig. 19 shows the low lying Sm 152 excitation spectrum deduced from the available data43), including both multiple Coulomb excitation and radioactive decay scheme measurements, decomposed into rotational bands. It should be emphasized that the spin and parity assignments of many of the upper levels shown here have not been established rigorously through correlation or equivalent measurements but are based on

4+--

i

1030 I I 34.0 I I

J

8+ -

T

~

i

1187keV

I 1057

I

2

i'l 75,5'1 963

000

2+

II

'.l

ii087

6+ IJ

r

9 5

I

:

3~

i

au

I

444 ! I

ii

563~

I j

;689;

1

! i

1395keV

236 ,007

;i 'J

~480

I

I i

869 10281 " ! H!I4 12173

707 i

935

340

IF

690 I

Ji

I i

I 4+ ~ - -

'

367

245 2 +

K = O nB=n;,.=O • = 5

K=O

n•=l n ; , = O X = 2 ~, = 2 2 . 0 3 k e y B = -0J71 keV

Fig. 19. The low lying excitation s p e c t r u m for Sm]52; a n u m b e r

variety of other measurements both on the g a m m a radiation and on the corresponding conversion electrons. Considering first the gamma radiation, both g a m m a - g a m m a and back scattered particle-gamma coincidence studies have been carried out. In the former by gating sequentially on transitions in the ground state band it is possible to isolate higher and higher spin states through their deexcitation branchings in the later; as predicted in current multiple Coulomb excitation theory, both octupole transitions and those involving high excitations and high angular momenta are en-

I 122 122 o+t' o K:O n#=%=0),,:2 A = 2142 keV B=-0.194 keV C = 0 . 0 0 2 0 keV

i K=2

nB:O

nr:l;k=2

A • 3 0 6 7 keV B : - 0 3 3 keV

of higher intrinsic excitations have been omitted for clarity. the characteristics of the corresponding deexcitations. The octupole states were identified through their characteristic enhancement in particle-gamma spectra and their excitation functions. It is interesting to note that the octupole moment of inertia is very significantly larger than the quadrupole moments as might be anticipated on simple physical arguments; as measured it is roughly equal to the rigid moment expected for Sm 152. As an example of the advantages inherent in the multiple excitation studies, having only the 4 + and 2 + members of the ground state band a vibration rotation

175

N U C L E A R S T R U C T U R E STUDIES W I T H H I G H ENERGY HEAVY IONS -103

FR2

E = A[I(I+I)-KIK+I)] + B[I2(I+I) 2 KZ(K+II2 ] ~

'i

y-PARTICLE COINCIDENCE SPECTRUM

65 MeV

270

016 on T b '59

306

,/ /

/x . . . .

/

/

xJ

/,x- - -x /

~t---¢/ _xt.--~__± 20 40

1

60

II[+~)

1

I 80

I00

-~÷ ~

351

.L 120

1

t40

1495 k~V

862 •y-SINGLES

~ .t'. ~ .

k ~,,,,#~ SPECTRUM-- -~%~

1--66, 127o "~*-'r---- ~ 3 6 3

ABSORBER: (1030 IN3 Cu TARGET: 0.020 INS

50

~

"~

IOO CHANNEL NUMBERS

-

~

i 150

7

183

103

j 200

Fig. 20. Direct and coincidence gamma radiation spectra from multiple Coulomb excitation of Tb 159 with oxygen ions.

B o f - 0 . 1 4 0 keV is indicated, whereas having the higher members, the need for a cubic t e r m a n d a p a r a m e t e r B o f - 0.194 keV results. F r o m studies on the detailed b r a n c h i n g ratios in the deexcitations o f the beta and g a m m a b a n d s o f this nucleus, G r e e n b e r g et al. 43) have recently r e p o r t e d t h a t it is possible to a c c o u n t b o t h for the m a g n i t u d e o f the v i b r a t i o n r o t a t i o n term, and for the corrections to the well k n o w n A l a g a intensity rules relating to the interb a n d transitions, by mixing o f the g r o u n d state and b e t a v i b r a t i o n a l b a n d wave functions. This represents the first detailed e x a m i n a t i o n o f such a situation since previously an a d e q u a t e n u m b e r s o f i n t e r b a n d transitions had not been available. In a c c o r d with earlier estimates, G r e e n b e r g et al. 43) have f o u n d t h a t mixing o f the g a m m a v i b r a t i o n a l a n d g r o u n d state r o t a t i o n a l wave functions can a c c o u n t for at most some 10% o f the observed perturbations. Extension o f such measurements to other nuclei to trace the b e h a v i o u r o f this mixing as a function o f the nuclear d e f o r m a t i o n s involved will provide crucial i n f o r m a t i o n on the previously ignored higher o r d e r corrections to the nuclear collective motion. It m a y be o f interest to note t h a t in a series o f measurements carried out using the O a k R i d g e E N t a n d e m accelerator 44) oxygen b e a m at 49 MeV, we

have f o u n d an empirical factor o f roughly 200 relating the coincidence d a t a o b t a i n a b l e in given time using our i n s t r u m e n t a t i o n with the t a n d e m and the H I L A C using 0 16 ions o f the same energy. Recent measurements at Yale by G r e e n b e r g et al. 4s'46) have identified, for the first time to our knowledge, evidence for third o r d e r Coriolis p e r t u r b a tions in nuclear motion. Fig. 20 illustrates multiple C o u l o m b excitation studies on a Tb ls9 target, d e m o n strating the advantages o f the p a r t i c l e - g a m m a coincidence m e a s u r e m e n t s in disentangling the excitation spectrum. A l s o included in this figure is the g r o u n d state r o t a t i o n a l b a n d deduced f r o m these spectra, and f r o m g a m m a - g a m m a coincidence measurements, as well as a 43) j. S. Greenberg, G. C. Seaman, E. V. Bishop and D. A

Bromley, Phys. Rev. Letters 11 (1963) 211. 44) J. S. Greenberg, G. C. Seaman, D. A. Bromley and F.

McGowan, (to be published). 45) j. S. Greenberg and E. V. Bishop, Bull. Am. Phys. Soc., Set. II 6 (1963) 431. 46) j. S. Greenberg, D. A. Bromley, G. C. Seaman and E. V. Bishop, Direct interactions and nuclear reaction mechanisms, ed. by E. Clementel and C. Villi, (Gordon and Breach, 1963) p. 941 ; Proc. of Asilomar Conf. on Interactions of Complex Nuclei, ed. by Ghiorso, Diamond and Conzett, (Univ. of California Press) 1963. VI. E X P E R I M E N T A L T E C H N I Q U E S

176

D. A. B R O M L E Y

plot of the excitation energies in appropriate units 1). The systematic oscillation of this plot prompted a search for the perturbation responsible, leading to the above mentioned third order Coriolis effect. The odd-A Hamiltonian may be written as against J(J +

[ 40ol-

PROTON

ENERGY

SPECTRUM

Li B ON POLYETHYLENE

/

(C-A

DETECTOR -- YALE)

OEp Q=O = 27.3 MeV

ELi G = 63 MeV

OLAB=20* Q= -2.18

(17) where R represents the rotational angular momentum, I the moment of inertia, p the odd nucleon momentum and V, the nucleon-core potential. If the nucleon is in an orbit characterized by./, and the total nuclear angular momentum is J it follows that H may be written as h2

H=yZ

( j 2 + j2 _ 2 J i . Jl)

i,

= H R+Hp+H

p2

+v'

(18)

h2

axial approximation

_

~ 200 •,

-\

100I-

o

I I0

I 20

I_ 50

I 40

I_ 50

/ 6o

"-t,. 70

(20)

Fig. 21. Response o f a C-A semiconductor detector to protons from the Li 6 + CH 2 interactions.

(21)

functions Xo of Hp; the Coriolis coupling is ignored in first order and the state wave functions written as

(22)

T = XoDMr + (-- 1)J-Jz_oD~t_K,

h2

2]=~-[J(J+l)-2K2],

j

[Jl"Jl +J2"J2].

80

CHANNEL NUMBER

h2

I

•

we take

h2 . p2 Hp = 21 ) "j + 2-m + V,

He-

~blO

09)

-/3 = J 3 ; /3 = 0 ; 11 = 12 = /, w h e n c e t h e a b o v e r o t a t i o n a l , p a r t i c l e a n d C o r i o l i s t e r m s in t h e H a m i l i t o nian become respectively:

HR=~[J'J--2J

Ep = 23.5 MeV

-

c.

If we make the customary

o,oo d i

Normally the particle motion is treated in an appropriately non-spherical potential, V, to give the eigen-

(23)

using the usual symmetric top functions D~K to introduce the rotational motion. The Coriolis term is then

TABLE 3 G r o u n d state rotational bands for Tb ll9 and H o 165 Tb159

Ho165

E = Eo + A I ( I + 1) + BI2(I+ 1)2 q- C(-- l)Z-J (l + ff) (I + ½ ) ( I - ½ )

E = Eo + AI(I+ 1) + B F ( I + 1)2 + C ( - I ) 7 (1+7)(I+5)(I+3)(1+½)(I½) (I-- 3) (I - -~-)

A = 11.59

B = --0.0054

C = -0.006

A = 10.76

B = -0.0044

C < 2 × 10-7

Spin

Eexp.

Ecal¢"

Spin

Ecxp.

Eealc"

2/3 5/2 7/2 9/2 11/2 13/2 15/2 17/2 19/2 21/2 23/2

0 58 138 241 363 511 669 862 1053 1285 1498

0 58 138 241 363 511 67O 861 1053 1285 1500

7/2 9/2 11/2 13/2 15/2 17/2 19/2 21/2 23/2

0 95 210 345 500 671 861 1067 1289

0 95 211 346 500 672 861 1066 1287

NUCLEAR

STRUCTURE

STUDIES

WITH

HIGH

ENERGY

HEAVY

177

IONS

tO5

632K

-

I

S,;R

i

:

.

.

.

.

.

i04

1

J

z

,

I

i

io"

F

i

+

j

I

I

-,

......

1720C

ENERGIES ARE THOSEOF THE GAMMATRANSITIONSIN KeY

i02

'

K

INDICATES INTERNALLY CONVERTED K ELECTRONS

L

INDICATES !NTERNALLY CONVERTED L ELECTRONS

~ /

i

--

C INDICATES COMPTON EDGE

/

I i

__

[

20

40

60

BO

I00

120

140

160

180

200

220

illl

240

260

3~

280

!

[

320

340

I

~60

380

CHANNEL

Fig. 22. Response of a C-A semiconductor detector to conversion electrons and gamma radiation from a Bi206 source. I

,sooI ENERGY RESPONSE ,6ooL i

OF D R I F T E D

DETECTOR

(PEAKS OF KNOWN ENERGY TAKEN FROM Bi 206 SPECTRUM)

I?20C

~ ' ~1?20K

I

,4oo~ 1

~

I200~-

1 0 9 9 K / / / 1020K 895L / ' ~ 895K/~'~

I000~

800 L 803C 600,

i 400'

I

632K

497L J / 516K ./'/(~57K 398L -~'~516L 516C . j . / " f 5 3 7 K 3 4 3 K ~ ' K ~ " -34~'L 497K

803K~/a~l~

.~881C

K iNDICATES CONVERTED K ELECTRONS L INDICATES CONVERTED L ELECTRONS C INDICATES COMPTON EDGE

2oo~./ /

/'~

184L

f

°l

5kO

I00

I;o

E;o

s;o

2;0

5;0

.oo

CHANNEL

Fig. 23. Linearity plot corresponding to fig.

introduced as a perturbation operator on these approximate solutions. U s i n g the standard matrix elements given by Bohr47), for example, the peturbation energies m a y be written a s follows 48) for states o f angular m o m e n t u m J: First order AE (') = ( - 1)s+~(J + ½)a6r,~, (24)

22.

s e c o n d order AE(2) =

1

h2

~E " l - [ J ( J + 1) - 2 K 2 ] ,

(25)

47) A. Bohr, Dan. Mat. Fys. Medd. 26 (1952) 14. 48) We are indebted to J. Weneser for detailed discussions concerning this treatment. VI. E X P E R I M E N T A L

TECHNIQUES

178

D. A. BROMLEY

cluded by the high flux o f scattered heavy ions and the intense neutron and g a m m a background in the vicinity of the target. . .../// //

third order (for K = ~) AE(3)=I (h2) 3~/ (6E)~ • (-- 1) J+k

"

. ((j})

• (j _ ½) (j + ½) (j + 3) = C(-1)s+k.(J-½)(J+½)(J+3)

(26) •

ETECTOR~ --r

(27)

Here 6E is an average energy denominator ~ 500 keV; ( j ) is a matrix element of order unity• The decoupling parameter a appearing in eq. (24) is well k n o w n in K = ½ bands• The fact that the perturbation energy in eq. (25) has the rotational f o r m of eq. (20) is p r o b a b l y o f fundamental importance to the whole question o f nuclear collective m o t i o n as emphasized by Kerman, Kline and others. The perturbation term in eq. (27) appears to account for the observation o f fig. 20 in rather excellent fashion as illustrated in table 3, which also illustrates the anticipated unimportance of the equivalent seventh order effect which would be required to couple the K = + 27- wave functions involved in Ho 165. Extension o f such studies to other areas o f the periodic table would again be of great importance in furthering our understanding of the bases and limitations o f the collective models now in use. In recent years, extensive measurements have been carried out by the Berkeley H I L A C group 49) using a magnetic spectrometer to study the conversion electrons following multiple C o u l o m b excitation• This technique has the advantage o f much higher inherent energy resolution and the disadvantage that it is not susceptible to coincidence studies and that it is intrinsically a single channel device necessitating point by point scanning of the conversion spectrum. Recent development by C h a s m a n and Allen 5°) in our laboratory, a m o n g others, o f reliable, thick, surface barrier, lithium drifted, semiconductor detectors has made possible a major advance in the conversion electron technique• Fig. 21 illustrates 5°) the response o f a 5 m m thick Chasman-Allen detector to protons at r o o m temperature; fig. 22 is a corresponding spectrum o f conversion electrons 51) and g a m m a radiation from a Bi 2°6 source and fig. 23 demonstrates the linearity o f energy response obtainable in such measurements. Direct use o f such a broad range detector for the multiple C o u l o m b excitation conversion electrons clearly offers marked advantages, however it is pre49) R. M. Diamond, B. Elbeck and F. S. Stephens, Nuclear Phys. 43 (1963) 560. ~0) C. Chasman and J. P. Allen, Bull. Am. Phys. Soc. ; Nucl. Instr. and Meth. 24 (1963) 253. s0 C. Chasman, J. P. Allen and R. Chasman, (to he published) 1963.

__

ELECTRON TRAJECTORIES

I N C I D E N T SEAM

TARGET

/ / /,MAGNET POLE / , / / ~ / ," / . . / / / / / /

,ooo--

K,L 548 5 6 MeV

016on Au ~gz

,oo

K,LeM 1 0 6 0 I

K,L,M 570 [I

~.

'°°° I

J

,oo Bi 2°7

,o

SOURCE

SPECTRA

I 40

80

240 CHANNEL

NUMBER

Fig. 24. Schematic illustration of a broad range conversion electron detector system. As indicated, the upper spectrum was obtained from a gold target bombarded by 56 MeV 016 ions. The lower is a spectrum measured from a Bi207 source.

NUCLEAR

STRUCTURE

STUDIES WITH

Burginyon and Greenberg s2) have overcome this difficulty by inserting both target and detector in a strong transverse magnetic field which focuses the conversion electrons, approximately achromatically, onto a remote shielded semiconductor detector. Fig. 24 illustrates this new device s2) and shows a conversion spectrum obtained from 56 MeV 016 bombardment of gold in addition to a Bi 2°7 source spectrum. Because this device effectively reduces the solid angle for g a m m a radiation originating in the target, as opposed to the conversion electrons, it considerably simplifies the spectra through reduction of the Compton edges. In the prototype model shown here, where the targetdetector separation is 5 cm, reduction factors of 10 and 3 are obtained for 0.5 and 1.0 MeV g a m m a radiation respectively. These factors may be increased by increasing the target-detector separation, and the interposed shielding to a lesser degree, without significant reduction of the electron collection efficiency. This device shows high promise of combining the high resolution and broad range advantages of the magnetic conversion spectrometer and of the N a l scintillation spectrometer respectively for work in Coulomb excitation and a larger, more completely engineered unit is now under design. The Coulomb excitation studies described here represent only the initial steps in a concentrated attack on previously ignored aspects of nuclear collective motion which become accessible via the multiple Coulomb excitation approach. The characteristics of the Emperor tandem accelerator are almost ideally suited to this program.

7. Conclusion The intent of this paper has been to demonstrate, with examples selected from current heavy ion studies, some

HIGH ENERGY HEAVY IONS

179

of the unique advantages which these have for elucidation of areas of nuclear structure and behaviour which would otherwise be ascessible with difficulty, if at all. Collective phenomena have been shown to be accessible both through inelastic nuclear scattering and through multiple Coulomb excitation measurements. Cluster and multi-particle configurations are conveniently studied through single and multi-nucleon transfer reaction studies. These, in turn, yield both spectroscopic and reaction mechanism information. It should be emphasized that these examples represent at most a very restricted sampling of contemporary heavy ion research; space does not permit a more complete catalog. The advance which the Emperor tandem will mark in the instrumentation for these studies is obviously very great; the scope of instrumentation which has been evolved for use with existing heavy ion accelerators will be correspondingly extended. It appears reasonable to predict that contrary to general expectations even a few years ago, heavy ion reaction studies will constitute one of the most active areas in nuclear structure research in future.

Acknowledgements I am greatly indebted to my colleagues E. R. Beringer, C. Chasman, G. T. Garvey, and J. S. Greenberg, of the Yale Heavy Ion Accelerator G r o u p for their cooperation and assistance and to E. V. Bishop, J. C. Hiebert, R. W. Ollerhead, M. W. Sachs, G. C. Seaman, and A, M. Smith who in their dissertation research on the Heavy Ion Accelerator, have provided much of the material included herein. 52) G. Burginyon and J. S. Greenberg, (to be published) 1963.

VI. E X P E R I M E N T A L

TECHNIQUES