Competition of two-step processes in the reactions 60,62Ni(p, t) leading to unnatural parity states

Volume 63B, number 2

PHYSICS LETTERS

19 July 1976

COMPETITION OF TWO-STEP PROCESSES IN THE R E A C T I O N S 60,62 N i ( p , t) L E A D I N G T O U N N A T U R A L P A R I T Y S T A T E S M.J. SCHNEIDER*, J.D. BURCH and P.D. KUNZ Nuclear Physics Laboratory **, Department of Physics and Astrophysics University of Colorado, Boulder, Colorado 80309, USA Received 22 May 1976 Coupled channels calculations are done and compared to data for the reactions 6°,62Ni(p,t) at Ep = 27 MeV leading to four unnatural parity states. It is shown that (p,d) (d,t) and (p,p')(p',t) two-step mechanisms adequately describe the data for three of the four transitions, with the former being the generally dominant mechanism. It is well known [1 ] that excitation of unnatural parity states is forbidden to first order for the zero range description of the (p,t) reaction and thus provides a means of studying two-step processes unimpedded by the presence of a strong direct process. Higher order processes may also contribute significantly to the amplitude for natural parity (p,t) transitions [2] and holds the promise of resolving some of the difficulties in the DWBA analysis of these transitions. It is the purpose o f this note to demonstrate that the following two-step reaction mechanism, (1) sequential transfer, (p, d)(d,t) and (2) inelastic scattering plus double neutron transfer, (p, p')(p', t) and ( p , t ' ) ( t ' , t ) account very well for the population of three unnatural parity states in the nickel isotopes. These two mechanisms are illustrated for the 62Ni(p,t) reaction in fig. 1. It has been pointed out [2] that, neglecting spin-orbit effects, the angular distributions for these two processes are quite dissimilar at forward angles. The sequential transfer is generally non-zero at 0 ° and the inelastic excitation plus double transfer is zero at 0 °. In previous analyses of this sort, sequential transfer of two neutrons was found to account well for a forbidden (p,t) transition in 208pb [3], inelastic scattering plus dineutron transfer processes were used to reproduce an unnatural parity (p,t) transition on 22Ne [4], and both processes were used to reproduce similar data on 180 [5]. We show in the present paper that in the Ni isotopes, except for back angles, the sequen* Present address: Krasdale Foods Corp., Bronx, N.Y. 10474. ** Work supported in part by the U.S. Energy Research and Development Administration.

tial transfer process is the preferred mechanism for the population of the unnatural parity states although in one case the inelastic plus dineutron transfer makes important contributions. The 60,62Ni(p,t) experiments were done at the University of Colorado [6] with a proton energy of 26.8 MeV. Triton angular distributions were available for four unnatural states: the 2.63 MeV 3 + state in 60Ni, and the 2.90 MeV 1+, 3.42 MeV 3 + and 3.78 MeV 3 + states in 58Ni. The three 3 + states were clearly resolved from nearby allowed states, whereas the 1+ state had to be separated by a Gaussian peak-fitting routine [7] from the strong 2.94 0 + state. Angular distributions for these four states, along with results of calculations described below, are shown in fig. 2. The reaction calculations were done by secondorder DWBA with the computer code CHUCK [8]. The proton and triton optical parameters used throughout were set P1-T1 of Baer [9], which were found to give best reproduction of the shape of the 62Ni(p,t) ground state angular distribution. The deuteron optical parameters were the r 0 = 1.1 fm set of Childs [10] for the nickel isotopes. Thus the optical parameters for the three "projectiles" were of matched geometry and are listed in table 1. Two other sets of optical potentials were tried to see what sensitivity the calculations exhibit to optical model parameters. These are also given in table 1. The results for the three sets are shown in fig. 3, where a comparison is made for the case of P3/2 neutron pickup followed by fs/2 neutron pickup. It is seen that the position and height of the maximum does not change, and that there are moderate effects at large angles only. The usual non-locality corrections to the distorted 129

Volume 63B, number 2

PHYSICS LETTERS

INELASTIC+DOUBLE

19 July 1976

SEQUENTIAL PICKUP

PICKUP

(p, d) (p,

2 + mm~m

t ~ j~.

-

3+

I/2-

I(', " ) , I

Pf/2 '''''~

2+ JP3/2

tp, p')

62Ni

60Ni

g.s. O+

g.s. O+

(d, t)

62Ni

~fs/z

3/2-

)"

f5/2

61Ni

g.s. O+

60Ni 3+

(FOUR STATES OF EACH j " INCLUDED)

Fig. 1. The two two-step mechanisms contributing to the population of the unnatural parity states in 62Ni(p,t)6°Ni, 3 ÷. Shown schematically are the channels through which the two-step reactions proceed. Table 1 Optical model parameters used in the coupled channels calculations. Units are MeV or fm, as appropriate. The second and third sets listed in the table were used in only one calculation to indicate parameter sensitivity for (p,d) (d,t) calculations. The second triton set was altered from ref. [ 3] to optimally fit the appropriate elastic triton data of ref. [ 12] VR

r

aR

Set 1 Proton Deuteron Triton

55.4 99.9 165.4

1.12 1.1 1.16

0.78 0.82 0.75

Set 2 Proton Deuteron Triton

46.5 88.5 155.32

1.2 1.2 1.24

0.72 0.75 0.68

Set 3 Proton Deuteron Triton

54.1 99.9 149.0

1.10 1.1 1.27

0.77 0.82 0.66

VI 3.2

4 WD

rI

aI

Vso

rso

a so

rco

Ref.

25.8 66.3

1.32 1.32 1.50

0.59 0.70 0.82

24.8 11.26

0.98 0.92

0.75 1.0

1.25 1.3 1.25

[9] [10] [9]

25.96 72.4

1.32 1.29 1.43

0.58 0.66 0.85

24.8 11.26

1.06 0.92

0.68 1.0

1.25 1.3 1.25

[ 11 ] [ 10] [3, 12]

21.5 66.3 17.25

1.3 1.32 1.58

0.60 0.70 0.88

11.26

0.92

1.0

1.2 1.3 1.25

[13] [10] [13]

16.4 3.22 26.37 3.24 27

waves were made [8]. The well g e o m e t r y for the transferred nucleons was r 0 = 1.17 fm, a = 0.75 fm, f r o m the global fit o f Becchetti and Greenlees [11 ], and the well depths were adjusted to fit the nucleon binding energies. All calculations were done in zero range, since it appears that finite range effects are small w h e n the direct process is f o r b i d d e n [14]. The conventional transfer reaction strengths were used: 130

D~)'d = - 1 2 2 MeV fm 3/2, D~ 't = - 1 8 2 MeV fm 3/2 and D p't = - 5 0 0 fm 3/2 . In the Ni isotopes configuration mixing is important and we take it into account explicitly by using the shell m o d e l wavefunctions o f Glaudemans et al. [15]. The w a v e f u n c t i o n s consider the active neutrons to o c c u p y the three orbits 2p3/2, lfs/2 and 2pt/2. Core excitations are ignored, and the basis is not limited by

Volume 63B, n u m b e r 2 I

PHYSICS LETTERS

I

I

I

I

÷~lll~

19 July 1976

I

60Ni 2 . 6 2 5

62Ni(p,t}

3+

I.O

SEQUENTIAL PICKUP

~

+

~

Set L .... Set 2 ......... Sel 3 - -

(P3/z-f~/2) 3"

~ "0

O.I

/,SJ/NELASTIC + DOUBLE PICKUP sS S/

Ibo,

,

,~b°

(~cll 0.5

Fig. 3. Calculated cross-sections for the reaction 62Ni(p,t) 3.63 MeV 3 ÷ using the three different optical model parameter sets o f table 1 and proceeding here only by the sequential pickup of a P3/2 and a fsr2 neutron. Spectroscopic amplitudes are a s s u m e d to be 1.0 in all cases.

INELASTIC + ,,,sDOUBLE PICKUP "

O.I

+÷+÷

I.O

A

58Ni

"tlb 0.1

artificial restrictions on seniorities or occupation numbers. The calculated wavefunctions are complex and highly mixed, with, for example, 33 components being used to describe the 1.17 MeV 2 + in 62Ni. The wavefunctions provide a good account of ground state binding energies, level structures, M1 and E2 transition rates and single particle transfer strengths for data on 57-66Ni isotopes. Relevant to our work, Glaudemans et al. point out [15] that the higher levels in 58Ni more than likely suffer from omission of particle-hole pair components in the 56Ni core. For sequential transfers, the amplitudes were calculated assuming the transition to occur via each of the four lowest states of each possible J'~ in the intermediate nucleus, and then summed. Generally, most of the transfer strength was through the lowest intermediate state of each J~. With the single nucleon transfer strengths given, the normalization of the sequential transfer process is fixed. On the other hand, the excitation of the levels in 6°Ni by inelastic scattering plus two-nucleon transfer requires that inelastic scattering strength be adjusted by fitting the 62Ni(p,p') 2 + 1.1 7 MeV transition. With the explicit wavefunctions of Glaudemans et al., it was found that a strength

÷ + 3.775

3+

INELASTIC + DOUBLE PICKUP . , . . ~ ' - - - ~ s p~"

SEQUENTIAL ~lCKUPj ~ . ~

s S

/ I.O

~,/~

j

58Ni 2.902 I +

O.I

I

IO

I

20

I

30

8c.m.

I

40 (DEG)

I

50

1

60

70

Fig. 2. Cross-sections for the reaction 60,62Ni(p,t) leading to four unnatural parity states. Sequential pickup (lower solid line) a n d inelastic plus double pickup (dotted line) calculations are shown for each state. The top solid line for the SBNi 3.42 MeV 3 ÷ a n d the 58Ni 2.902 MeV 1 ÷ describes the s u m of b o t h mechanisms.

131

Volume 63B, number 2

PHYSICS LETTERS

of V0 = 295 MeV was required for a 1 fm range Yukawa potential. This is somewhat larger than the strength of 244 MeV found by Satchler [16] in fitting proton inelastic scattering on 92Zr. However, for the 58Ni(p,p') excitation to the 2 + state a strength of 200 MeV was needed to fit the inelastic data and was used in (p,p')(p',t) calculations. The (p,t) reaction to the lowest 2 + state of the residual nucleus followed by (t,t') to the 3 + state of interest was also considered. The triton nucleon interaction was taken to be of Yukawa shape with the same rms radius (2.82 fm) and volume integral as the Gaussian triton-nucleon interaction used by Ascuitto and Glendenning [13]. Its strength was 248 MeV. The (p,t) (t,t') process was calculated to yield a maximum cross-section of 0.34 nb/sr for the 60Ni 3 + state at 2.63 MeV and hence was not considered further. Results of the two-step DWBA calculations are shown in fig. 2. The angular distribution of the 60Ni 3+ state at 2.63 MeV is accompanied by two curves, representing the sequential transfer and inelastic scattering plus double pickup hypotheses. The former process gives fine agreement with data and the latter appears to give little if any contribution. Addition of these two calculations was not attempted, Although the magnitude of this transition is very well predicted, there is some disagreement in phase between data and calculation which is not understood at present. It is important to use realistic wavefunctions. This is shown by the fact that calculations done with a naive approximation (i.e. 62Ni g.s. = 1/X/~ [(fs/2) 4 (pa/2) 2 + (fs/2)2(pa/2)4]) overestimate the cross-section for this state by a factor of about 2.5. A slightly better approximation, which uses only the two largest terms in the wavefunctions of all relevant states, yields an underestimation of this cross-section by about 50%. The additional terms in the shell model configuration all add constructively in the sequential transfer to agree with the experimental cross-section. The sequential transfer hypothesis also accounts well for the angular distribution of the 58Ni 3 + state (at 3.42 MeV) at low angles, with some contribution from (p,p')(p',t) at high angles. The sum of these contributions, added incoherently, is also shown. Incoherent addition of these two processes is adequate because the former is primarily S ---1, while the latter is mostly S---0 [2]. The 2.63 MeV 3 + state is populated almost entirely through fs/2 and P3/2 particle 132

19 July 1976

transfer, and the 3.42 MeV 3 + state, whose configuration is pure (fs/2,P3/2) 3+, has no other contributions at all. The sequential pickup calculation for the 3.78 MeV 3 + state, which consists of fs/2 and Pl/2 transfer, fails. This state is the likeliest of the three to suffer from the previously mentioned neglect of possible f7/2 excitations, and we speculate that this omission is responsible for the failure of the calculation here. The (p,p') (p',t) calculation also falls far short of reproducing the data for this state. The 2.90 MeV 1+ state of 58Ni shown in fig. 2 is especially interesting because both two-step mechanisms, again added incoherently, appear to be equally responsible for its excitation. We believe that only one other case of cooperation between two-step mechanisms has been seen in the (p,t) reaction [5]. We conclude that excitation of three out of the four unnatural parity states seen in the present experiment is well accounted for by the sequential transfer mechanism, with a large contribution from the inelastic scattering plus double transfer mechanism for one of the states. A plausible explanation is given for the failure of the calculation for the other. The "moderate collectivity" of the nickel isotopes thus exerts itself not in strong inelastic scattering coupled to double transfer, but in sequential transfer where there is strong constructive interference between the various shell model configurations. Most important is the fact that no renormalizations were necessary after calculational parameters were fixed from independent sources. Assuming the validity of the calculation procedure, renormalizations would suggest either that the wavefunctions were inadequate or that additional reaction mechanisms were important. The success of these calculations further suggests that nonorthogonality effects [5] and continuum states of the deuteron, neither of which was considered herein, may not have much effect on (p,t) transitions to unnatural parity states. We are grateful to J.E. Koops and P.W.M. Glaudemans of the Rijksuniversiteit Utrecht for providing the wavefunctions used herein.

References [1] B.F. Bayman and D.H. Feng, Nucl. Phys. A205 (1973) 513.

Volume 63B, number 2

PHYSICS LETTERS

[2] T. Udagawa and D.K. Olsen, Phys. Lett. 46B (1973) 285. [3] N.B. de Takacsy, Nucl. Phys. A231 (1974) 243. [4] D.K. Olsen, T. Udagawa, T. Tamura and R.E. Brown, Phys. Rev. C8 (1973) 609; W.S. Chien et al., Phys. Rev. C 12 (1975) 332. [5] H. Segawa, K.I. Kubo and A. Arima, Phys. Rev. Lett. 35 (1975) 357. [6] J.D. Burch, M.J. Schneider, J.J. Kraushaar and P.O. Kunz, to be published. [71 D.H. Zurstadt, Univ. of Colorado, unpublished. [81 P.D. Kunz, unpublished. [9] H.W. Baer et al., Ann. of Phys. 76 (1973) 437.

19 July 1976

[10] J.D. Childs, W.W. Daehnick and M.J. Spisak, Phys. Rev. C 10 (1974) 217. [11 ] F.D. Becchetti and G.W. Greenlees, Phys. Rev. 182 (1969) 1190. [12] E.R. Flynn et al., Phys. Rev. 182 (1969) 1113. [13] R.J. Ascuitto and N.K. Glendenning, Phys. Rev. C 2 (1970) 1260. [14] L.A. Charlton, Phys. Rev. Lett. 35 (1975) 1495. [15] P.W.M. Glaudemans, M.J.A. De Voigt and E.F.M. Steffens, Nucl. Phys. A198 (1972) 609; J.E. Koops, private communication. [16] G.R. Satchler, Nucl. Phys. A95 (1967) 1.

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