The 54Fe(p , d)53Fe and 140Ced(p , d)139Ce reactions at 122 MeVag

Nuclear Physics @ North-Holland

A441 (1985) 189-208 Publishing Company

THE “Fe(fi, d)“Fe

S.A. DICKEY, Nuclear Physics Laboratory+,

140Ce($,d)139Ce REACTIONS

AND

J.J. KRAUSHAAR

Department

and

AT 122 MeV

J.R. SHEPARD

of Physics, University of Colorado, Boulder, CO 80309, USA and

D.W. Department

MILLER,

of Physics

W.W. JACOBS

and

W.P. JONES

” , Indiana University, Bloomington, IN 47405, USA Received

18 February

1985

reactions have been studied at a proton energy of The 54Fe(p, d)53Fe and ‘@Ce(p, d)‘%e 122 MeV. Analyzing powers and angular distributions were obtained for outgoing deuterons to the strong low-lying single-particle states in both nuclei. These data along with the data of others at have been compared with 26, 29, 41, 52 and 24, 35, 55 MeV for 54Fe and ‘@Ce respectively, exact-finite-range DWBA calculations carried out in a consistent fashion to determine the energy dependence of the spectroscopic factors. A strong energy dependence was noticed for the spectroscopic factors when the I-values were large.

Abstract:

E

NUCLEAR REACTIONS “‘Fe, ‘mCe(polarized p, d), E = 121 MeV; measured u.( 6), A( 0). 53Fe, i%e levels deduced spectroscopic factors. DWBA analysis. Enriched targets.

1. Introduction

The (p, d) reaction has been used extensively at energies below about 60 MeV to provide spectroscopic information on nuclear states. The reaction data coupled with a theoretical analysis using the distorted wave Born approximation (DWBA) in either zero-range or exact-finite-range has been a generally reliable source of information on the I-values and the spectroscopic factors involved in transitions to states of numerous nuclei. With the increased availability of higher energy proton beams the applicability of this conventional direct reaction mechanism to studies done with incident energies of 100 MeV or more has come into question. The use of higher-energy proton beams for the study of the reaction can lead to a more complete knowledge of the high-momentum components of the nuclear wave functions and provide information on deep hole states. Such data can also help explore the role of two-step processes at high energies and assess the importance of using the Dirac rather than the Schroedinger equation in the reaction theory. It was thus felt ’ Work supported +’ Work supported

in part by the US Department of Energy. in part by National Science Foundation grant no. PHY81-14339. 189

190

S.A. Dickey et al. / 54Fe, ‘40Ce(@, d)

important to understand whether conventional reliably for this new energy region. There reaction

have been

several

has been examined

studies

that relate

at several higher

DWBA

calculations

to this question. energies

can be used

The 13C(p, d)‘*C

but most recently

studies

at

123 MeV [ref. ‘)I, 200 and 400 MeV [ref. ‘)I and 800 MeV [ref. 3)] have explored the dependence of the reaction mechanism on energy. These works can be summarized by noting that the angular distributions for the lp,,* neutron pickup to the ground state and the lp,,, pickup to the 2+ level at 4.44 MeV seem well accounted for both in shape and magnitude at the various energies, while the analyzing-power data taken at 123, 200 and 400 MeV for the same states are in serious disagreement with the DWBA calculations. The 24Mg(p, d)23Mg reaction leading to the excitation of the $’ state at 2.36 MeV has also been a testing ground for the (p, d) reaction at higher energies since data exist at a number of energies between 27 and 185 MeV. Recent analyses “) of these data indicate that DWBA calculations account for the data reasonably well up to about 95 MeV but fail rather badly above that energy to account for either the cross section or the analyzing power data. Data on the “Zr(p, d)“Zr reaction has been examined ‘) over the energy range of 20 to 185 MeV. Here the spectroscopic factors for transitions with Z-values of 1 and 2 are approximately constant over the energy range, while there is more than a factor of 2 decrease in the spectroscopic factor for the strong I= 4 transition to the 89Zr ground state. There have been several efforts ‘,6,7) to analyze data from the *08Pb(p, d)“‘Pb reaction at energies up to 123 MeV. Strong energy dependencies were noted in these studies 6,7) for the spectroscopic factors for the f7,*, h9,2 and i,3,2 states. For example, the spectroscopic factor for the /= 6 transition decreased by a factor of 4 over the energy range and agreement ‘) between the analyzing-power data and calculations at 123 MeV was marginal at the best. Because ‘of these discrepancies it was felt worthwhile to make further measurements on the (p, d) reaction at energies around 120 MeV on nuclei that were in the middle of the mass table and where strong transitions to single-particle neutron states would be evident. To complement the existing data, 54Fe and 14’Ce were chosen since both of these nuclei have closed neutron shells and a fair amount of low-energy (p, d) data with these targets exist in the literature. The main purpose of the present study was a test of the reaction mechanism, and it was thus felt important to obtain analyzing-power data in addition to the cross sections. It is vital for a study of this kind to carry out the distorted wave calculations following some systematic procedure for obtaining the optical potential and the neutron bound state parameters. The comparison of spectroscopic factors found in the literature for studies done up to 20 years ago is of limited value because of the great variations in the details of the calculations. In order to carry out the calculations in a consistent way so that spectroscopic factors can be compared at various energies a standard set of bound state parameters have been adopted, a consistent set of

S.A. Dickey et al. / 54Fe, ‘“Ce(i,

191

d)

proton optical model parameters used as well as deuteron potentials based on the adiabatic approximation. In addition the calculations have all been carried out in exact finite range with non-local correction factors incmded. 2. Experimental method Measurements were carried out at the Indiana University Cyclotron Facility using a polarized beam of 122.4 MeV protons. The protons, produced in an atomic-beam source located in the 800 MV electrostatic terminal, were accelerated by the injector and main cyclotrons and transported to the QDDM magnetic spectrometer which was used in a dispersion matched mode. A helical cathode position-sensitive proportional chamber “) placed in the focal plane of the spectrometer detected the deuterons. Two plastic scintillators (0.63 and 1.27 cm thick) in back of the proportional chamber provided particle identification and helped reduce the background. The solid angle of the spectrograph was set at 2.312 msr and 1.44 msr for 54Fe and 14’Ce respectively. Beam polarizations were monitored by a 4He polarimeter, periodically inserted directly after the injector cyclotron. Typical beam polarizations were about +79% and -78% in the two spin orientations, with beam intensities on target of about 15 nA. The 54Fe target was a free-standing metal foil with an area1 density of 4.42 mg/cm* and 97.2% enrichment, while the 14’Ce target was a suspension of Ce20, in polystyrene with an area1 density of 3.74 mg/cm* and an enrichment of 99.7%. Representative deuteron spectra are shown in figs. 1 and 2. The resolution for both targets was approximately 200 keV full-width at half-maximum which was sufficient to resolve the states of major interest. Both cross-section and analyzing-power data 601111rrrrlllll “Fe (“p.d) 53Fe &,= 12”

Ln E Y40s 75 -

k:

&!

E, = 122.4 MeV

z ,q20::

400 Channel

600 Number

800

1000

Fig. 1. A deuteron spectrum at a laboratory scattering angle of 12” from the 54Fe(p, d) reaction. The numbers above the peaks are the energies in keV of the states populated by the more intense transitions.

S.A. Dickey et al. / 54Fe, ““Ce(j?, d)

‘40Ce(p’.d) ‘““Ce 8LAB= 20” E, =122.4 MeV

5

200

400 Channel

600 Number

800

,

1000

Fig. 2. A deuteron spectrum at a laboratory scattering angle of 20” from the ‘?Ze(p, d)%e reaction. The numbers above the peaks are the energies in keV of the state populated by the more intense transitions.

were measured for the 54Fe target in the angular ranges 8”~ B G 40” (A@ = 2’) and for the 14*Ce target in the range 6”~ 8 6 40” (A0 = 2”). The spectra for the two targets were analyzed by fitting a skewed gaussian peak shape, with a linear background, to the various peaks to determine their areas and centroids. The energies of the states in 53Fe and ‘39Ce were determined assuming the energies ‘*‘O) of the states in those nuclei that were well isolated and populated by strong transitions in the (p, d) reactions. The energies of the remaining states were determined by fitting a quadratic polynomial to the deuteron momentum as a function of channel number. In figs. 1 and 2 the energies in keV that are shown over the peaks are based for the most part on the more precise values listed in the Nuclear Data Sheets 9710).The integrated beam current used for the normalization of the data was obtained from a Faraday cup located in the scattering chamber. Dead-time corrections were determined by comparing the number of pulses from a pulser to the sum of pulses (processed similarly to the real detector pulses) in the observed pulser peak in the deuteron spectra. The error bars shown on the crosssection and analyzing-power data points in the figures were determined from counting statistics. Where no error bar is shown, the uncertainties are smaller than the dots representing the data. The uncertainty in the overall normalization of the data was estimated to be less than 15%. 3. Exact-finite-range

distarted wave calculations

All of the cross-section and anafyzing-power distorted wave calculations made for the two nuclei were done using the exact-finite-range code DWUCKS ‘I). In this

193

S.A. Dickev et al. / 54Fe, ‘40Ce(@, d)

way, any energy

dependence

as any deuteron

D-state

in the zero-range

contributions

normalization

were automatically

constant,

Dfj, as well

included.

The optical model parameters used in the calculations for the incident protons were of two types: for all energies below 55 MeV Becchetti and Greenlees I’) potentials were employed while at 122 MeV the Schwandt et al. 13) potentials were used. The deuteron parameters are based upon the adiabatic approximation i4). The potentials were made up of proton and neutron potentials ‘) taken at half the deuteron energy and combined according to the prescription of Harvey and Johnson I’). The optical model parameters used in the DWBA calculations are given in tables 1 and 2. The bound state wave functions were obtained assuming the picked-up neutron is in a fixed-geometry Woods-Saxon well with a depth varied to make the binding energy equal to the neutron separation energy. The spin-orbit term was taken to be 25 times the Thomas term. The geometrical parameters for the well were the relatively standard values of r, = 1.25 fm and a, = 0.65 fm. Non-locality corrections were included in the distorted waves. For the proton in the entrance channel and the bound state a non-locality correction factor of 0.85 fm was used, and for the deuteron in the exit channel a correction factor of 0.54 was used. The results of the distorted wave calculations as well as the cross-section and analyzing-power data for 54Fe and 14’Ce are shown in figs. 3 to 9. Before discussing the results in detail the existing (p, d) data on 54Fe and r4’Ce will be summarized.

4. Results and discussion As mentioned

in the introduction

there have been

several

earlier

studies

of the

54Fe(p, d)53Fe and 14’Ce(p, d)139Ce reactions at various energies between about 20 and 55 MeV. Aside from some early investigations 16,17*‘8)the results of the relevant 54Fe(p, d) studies are summarized in table 3. Also listed in table 3 is information on the adopted levels and spin and parity assignments from the nuclear data summary of Auble ‘). In order to provide more complete information on the 54Fe(p, d) reaction at a lower proton energy a study was conducted 19) at 26.4 MeV using the University of Colorado cyclotron and the energy-loss spectrometer. The spectroscopic factors that are listed for the 26.4 MeV data were obtained using the procedures outlined in sect. 3. With exception of the 122 MeV data the spectroscopic factors listed for the 54Fe(p, d) reaction studied by others at 29 MeV[ref. *‘)I, 40 MeV[ref. “)I and 52 MeV [ref. “)I are taken directly from the original work. Suehiro et al. 21) have carried out a number of distorted wave calculations with different optical model parameters for both the proton and deuteron. The particular spectroscopic factors listed in table 2 were obtained by them with proton parameters from Becchetti and Greenlees I*) and deuteron

parameters

from Perey and Perey 23).

P d :

40

122

55

35

122

d” :

:

P d

:

29

52

:

26

-51.38 -105.71 -44.98 -99.25 -25.91 -77.54

-23.69 -76.95

-44.79 -103.74 -41.00 -99.90

-48.36 -107.39

-49.19 -108.24

1

0.75 0.79 0.75 0.79 0.713 0.79

1.17 1.17 1.17 1.25 1.17

-8.12 -20.58

-6.14 -2.14 -8.74 -11.71

-3.68 -0.389

-3.11 -0.099

TABLE

0.63 0.56

1.36 1.29

2

0.75 0.79 0.75 0.79 0.713 0.79

-5.0 -1.56 -9.4 -6.0 -8.123 -14.74

20.44 70.88 0.44 50.72

1.32 1.26 1.32 1.26 1.36 1.29

0.63 0.63 0.63 0.63 0.63

-6.2 -6.2 -6.2 -6.2 -6.36 -6.2

-7.4 -6.2

0.54 0.55 0.54 0.56

8.8 74.04 58.04

0.54 0.56

1.32 1.29 1.32 1.29

1.32 1.29

19.96 82.84

-6.2 -6.2 -6.2 -6.2 -6.2 -6.2 -6.2

0.54 0.56

1.32 1.29

22.58 84.40

optical-model parameters used in the calculations

0.75 0.79

1.17

‘?Ie

0.75 0.79

1.17

1.17 1.17 1.17 1.17 1.25 1.17

TABLE 54Fe optical-model parameters used in the calculations

1.01 1.01 1.01 1.01 1.08 1.01

1.01 1.01 1.01 1.01 1.01 1.01 1.01 1.01 1.04 1.01

0.75 0.75 0.75 0.62 0.75

0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.62 0.75

$-

4’

g-,2-

y’-’ zz- ,z5-

($) _

3310

3

2840

3550

3

3 2

0

1

2043

3 I

I

3

3390

“) Ref. “).

(0.54),/a-(0,29),/z-

(1.00),,,-(o.52),,20.84

0.45

0.48

0.052

0.056

3.75 0.043

c2s

2967

2840

1328 1423 1696 2043 2339

0 741

0.47

0.050

0.052

4.6 0.048

C’S

‘) Ref. 22).

I

29 MeV ‘f

E (keV)

~-

TABLE 3

3

3

3892 4250

3

3

3 2

3 3 0

1

3

1

1

3

1

3774

3567

3333 3399

2839 2915 2976

2042

1423

0 745 776

E (keV)

40 MeV d,

54Fe(p, d)53Fe

2.11

0.04

0.04

0.30

0.58 0.97

0.39 0.06 1.31

0.66

0.08

3.48 0.05 0.01

C’S

on the levels of 53Fe and the results of studies

d, Ref. ‘I).

of information

26.4 MeV b,

1423

0 741

E (keV)

b, Ref. 19).

‘) Present work.

“) Ref. 9).

4256

3711

3040 3176 3321 3393 3462.9 3567

f-

0.0

741.1 774.4 1328.1 1423.5 1696.3 2043 2339.6 2419 2879 2845 2922 2961

;I$;$-

1”

E (keV)

53Fe Nuclear Data Sheets “) -.~

Summary

4235

3144 3833

3546

3351

3

1 (1)

3

(2)

0

3

2760 2890

1

(3)

3 1

f

2029

1409

0 744

E (keV) 3.0 0.06

C*S

1.6

0.03 (0.06)

0.3

(1.8)

1.2

0.3

0.04

(0.07)

52 MeV ‘)

4.256

3567

3333

;-

27--

;-

4’

Z2

2840 2967

$g3.. a

f 3z

i”

122 MeV ‘)

1423 1696 2043

0 741

E (keV)

- ~-

of the s4Fe(p, d)53Fe reaction

1.0

0.15

(0.55)

1.1

0.26

0.049 0.006 0.06

1.95 0.113

C2S

(b 11

&).’

1930

2

2

1610

$‘* (3,’ (% 2)” (I$)’

(1;’

2

1330

2 0 5

I

24.5 MeV b,

(I)* g+

0 252 750

3+ I ,+ 1 u2

0 255 154

1320 1347 1596 1630 1818 I842 1889 1907 1965 1984

E(keV)

1”

E (keV)

‘Te Nuclear Data Sheets “)

Summary of info~atio~

0.8

0.3

1.76

4.0 1.6 9.1

C2S

2

0

1790

1910

2

2

5

2 0

I

1600

1330

0 260 760

E (keV)

4

1.2

0.08

0.7

3.0

4.6 1.6 8.1

es

t930

1610

0 250 750 1030 1330

E (keV)

2

2

2 0 5 2 2

I

55 MeV d,

‘40Cefp, d)‘39Ce

1.1

0.46

4.0 2.0 10.2 0.33 2.20

C2S

1907

1320

0 25s 754

E (keV)

and the results of studies of the 14’Cefp, d)13’Ce reaction

35 MeV “)

on the leveis of “‘Ce

TABLE

l

j+ $”

.5* z

4’ $I.-

j+

J*

122 MeV “)

0.6,0.44

2.1

1.62 1.0 1.8

C2.9

P

9

s 3 gG

$

$ b n <

g

?

S.A , Dickey et al. / 54Fe, ‘40Ce($, d)

9 N

197

198

S.A. LXckey et al. / 54Fe, ‘“Ce(@, d)

In a similar

fashion,

information

on the (p, d) reaction

on 140Ce is summarized

in table 4. The adopted levels and spin-parity assignments from the data summary of Peker lo) are listed along with the results of studies at 24.5 MeV [ref. 24)], 35 MeV [ref. “)I

and

55 MeV [ref. ““)I in addition

to the results

of the present

work

at

122 MeV. The spectroscopic factors listed in table 4 for the work of others are also taken directly from the original publications. The values listed from the study of Chaumeaux et al. *“) at 24.5 MeV were normalized by them so that the transition to the t’ ground state had a value of C’S of 4.0.

4.1. THE 54Fe($, d)53Fe REACTION

AT 122 MeV

The angular distributions and analyzing-power data for the lower excited states of ‘*Fe are shown in figs. 3 to 6. The transition to the ground state is well isolated and is established to have Z=3 from the pickup of a 1fT12 neutron. The distorted wave calculations account for the data reasonably well except that the theoretical cross sections fall off with increasing angle somewhat more rapidly than do the data. The cross section at 8” appears to be low for most of the angular distributions. While a check of these data points did not reveal any necessary corrections, there is a possibility that an undiscovered normalization problem led to cross sections at that angle that were about 20% low. It can be seen in table 3 that the extracted value for the spectroscopic factor (C’S, = 1.95) is considerable below the other published values for the ground state transition. Other reasonably strong I = 3 transitions are known to occur to states at 2840, 3333, 3567 and 4250 keV. The angular distributions and the analyzing-power data for these four states are very similar to that for the ground state with the possible exception of the state at 3333 keV. There is a rather strong I = 2 transition to a state at 3390 keV in studies at 26.4, 40 and 52 MeV and it is evident from fig. 1 that the present experiment cannot resolve these two states. It is also apparent from the angular distributions and analyzing-power data that there are small differences between the data for the 3333 keV doublet and the other resolved I= 3 transitions. On the basis of the similarity of the analyzing-power data for the states at 2840, 3567 and 4256 keV, both to the ground state data and the theoretical calculations for a s- state, an assignment of spin and parity $- can be made for the first time to these states rather than the alternative choice of $-. There is also a weak I= 3 transition reported to a state at 1423 keV. This state is known to have a spin and parity of $- and in fact the analyzing-power data are quite different from the s- ground state, although the results do not closely agree with the $- calculation. There are two I = 1 transitions to states at 741 and 2043 keV that have been observed. The general slope of the theoretical angular distribution above about 15” is in reasonable agreement with the measured cross sections. Below 15”, however, there is a major deviation as the calculations rise very much more rapidly than do

S.A. Dickey

et a-11. / 54Fe, ‘40Ce($, d)

199

&,= 122.4 MeV

:_I\

E

lo* 0

IO

20

30

Bcm (deg)

40

50

0

IO

2043

keV

1

2840

keV

1

\

2967

keV

1

20 30 8 c m. (de@

40

50

Fig. 3. The angular distributions for the transitions to states up to 2967 keY in 53Fe. The solid lines are the results of distorted wave calculations that are described in the text.

200

S.A. Dickey et al. / 54Fe, ‘40Ce(fi, d)

256

keV

AT3

l*i,! 0

Fig. 4. The

IO

20 8 cm.

30

40

50

Meg)

distributions for the transitions to the higher-lying states in 53Fe. The solid lines are the results of distorted wave calculations described in the text.

201

S.A. Dickey et al. / 54Fe, 14’Ce($, d)

1.0.

’

,

8

,

I

1

’

-54Fe (b.d)53Fe zEp=l22,4MeV

a”

-1423

1

.*

*

1

keV 52840

%.,,

keV

.

(deg)

Fig. 5. Analyzing-power results for the S4Fe(b, d)53Fe reaction for states up to 2967 keV. The spin and parity were assumed to be s- for the states at 0.0, 1696 and 2840 keV, f’ for the state at 2967 keV, and +- for the states at 741 and 2043 keV.

the data as the angle is decreased. The calculations describe the analyzing-power data surprisingly well for the two states. The only other state of interest with respect to the present study is the one at 2967 keV which involves an I= 0 transition. Except for the sharp minimum around 25” the calculations describe both the angular distributions and analyzing-power data very well.

202

SA. Dickey et al. / 54Fe

JIG]

-1.0 i

0

IO

20 30 B c m (ded

40

50

Fig. 6. Analyzing-power results for the higher-lying states in the s4Fe(& d)“Fe reaction. The spin and parity were assumed to $- for the states at 3567 and 4256 keV.

4 .2. THE ‘40Ce($, d)‘39Ce REACTION

AT 122 MeV

There are a wide variety of I-values involved in the transitions in the (p, d) reaction to the low excited states of 139Ce.Three I= 2 transitions are observed to the ground, 1320, and 1907 keV states. All three angular distributions, which are shown in fig. 7, are well described by the calculations and the ground state analyzing-power data (fig. 8) agree reasonably well with the calculations for a 1’ state. The 1320 keV state is thought to have a $+ assignment and this is supported by the analyzing-power

S.A. Dickey et al. / “‘Fe, ‘40Ce(ji, d)

203

.*. Pi

lO3y

l

keV

1320

. 0

I I I IO 20

,

, 30

,

.

, 40

-

, 50

8 c.m (deg) Fig. 7. The angular

distributions of distorted

%,. for the transitions wave calculations

(dw)

to the states in ‘?e. The solid lines are the results that are described in the text.

204

S.A. Dickey et al. / 54Fe, ‘40Ce($, d)

1.0

.

1

.

'40Ce($,d)‘“‘Ce

,

* I

I

E, =122.4 MeV

-

0.0

Fig. 8. Analyzing-power results for ‘40Ce($, d)‘“‘Ce. The spin and parity were assumed to be $’ for the ground state and 1907 keV state, f’ far the state at 255 keV, y- for the states at 754 and 2286 keV, 5’ for the state at 1320 keV, and 3’ for the states at 2556 and 2840 keV (a $’ calculation is shown as a dashed line for these states).

data and calculations. The analyzing-power data for the 1907 keV state does not uniquely select either the g” or 2’ assignment. The I= 0 transition to the $+ state at 255 keV presents an angular distribution and analyzing-power data that are both in reasonable agreement with the DWBA calculations. There is a strong I= 5 transition to the yLi?-‘ state at 754 keV. The data are in

205

S.A. Dickey et al. / 54Fe, ‘40Ce($, d)

good agreement y- state is thought

with calculations

based

on the y-

to exist at 2286 keV. The angular

assignment.

distribution

Another

possible

and analyzing-power

data for this state cannot really confirm that assignment. There is a possible <’ state at 2251 keV, and it is likely that the present data represent an unresolved doublet. There are two possible I=4 transitions to states at 2556 and 2840 keV. The theoretical descriptions of the data are not very good, and it is likely that other states are making some contributions to the cross sections and analyzing-power data. Calculations for an assumed spin and parity of both $+ and f’ are shown in fig. 8 for these states. There appears to be a clear preference for the f’ assignment in contrast to the 3’ assignment assumed by others 23).

4.3. THE

ENERGY

DEPENDENCE

OF THE

SPECTROSCOPIC

FACTORS

The exact-finite-range distorted wave calculations were carried out as described in sect. 3 for the strong and isolated transitions in the case of 54Fe at 26.4, 29, 40 and 52 MeV as well as at 122 MeV. In the case of 14’Ce, cross sections were available only for the ground state for the data of Chaumeaux et al. so that only the data at 35 MeV and 55 MeV could be utilized. Tables 5 and 6 list the spectroscopic factors that have been extracted for the selected transitions in 54Fe and ““%e, respectively. In principle, if the assumed reaction mechanism and wave functions for the states involved are correct, the spectroscopic factors derived from the data at various energies should be the same. The 54Fe(p, d) spectroscopic factors listed in table 5

do in fact show an energy dependence. Considering the three clean I= 3 transitions involving an fT12neutron pickup (ground state, 2840 keV and 3567 keV) the averaged

TABLE The spectroscopic

factors

5

for the 54Fe(p, d)53Fe reactions at various using exact-finite-range calculations

energies

obtained

C’SQ E (keV)

0 741 1423 2043 2840 2967 3333 3567 4250

j”

;3I:3I:;+ IZI:-

I

3 1 3 1 3 0 3 3 3

26.4 MeV

29 MeV

40 MeV

3.75 0.043 0.056 0.052 0.48 0.45 0.53 0.29

3.45 0.038 0.056 0.039 0.39

1.95 0.026 0.046 0.033 0.27 0.49 0.36 0.15 1.22

52 MeV 1.41 0.034 0.035 0.027 0.19 0.46 (0.80) “) 0.18 1.oo

122 MeV 1.95 0.11 0.049 0.060 0.26 1.10 (0.55) “) 0.15 1.00

“) There are states at about 3333 and 3390 keV that involve I= 3 and 1= 2 transitions, respectively. The spectroscopic factors shown are for an I = 3 transition but there could also be appreciable contributions from the I = 2 transitions.

206

S.A. Dickey et al. / 54Fe, lace@, TABLE

The spectroscopic

E (keV)

0

255 IS4 1320 1907 2556 2840

6

factors for the 14’Ce(p, d)“‘Ce reaction at various range calculations

.?r J

2+

:+ &z 5+ (3f5,’ I7+.z9+ I7+,I9+

d)

energies obtained

using exact-finite-

CZS, I

2 0 5 2 2 4 4

35 MeV

55 MeV

122 MeV

3.4 1.8 7.3 2.0 (1.05,1.20) 1.8 2.1

1.8 1.1 2.5 1.1 (0.28,0.24) 0.44 0.90

1.6 1.0 1.8 2.1 (0.60,0.44) 0.80, 1.0 0.63,0.85

ratios at 26.4, 29,40, 52 and 122 MeV are 1.00: 0.87: 0.53: 0.47 and 0.52, respectively, with the ratio at 26.4 MeV set equal to one. Thus, a fall-off of about a factor of 2 is indicated as the energy is increased. On the other hand, the averaged ratios for I= 1 are 1.00: 0.82: 0.62: 0.66: 1.86 and for l=O 1: 00: -: 1.09: 1.02: 2.26. An increase of about a factor of 2 going from 26 to 122 MeV is indicated. It should be noted, however, that the increase is not monotonic since the ratio dips below one for the three middle energies. The i4’Ce(p, d) reaction displays somewhat the same features. Here almost all of the spectroscopic factors decrease with energy over the 35 to 122 MeV interval but the spectroscopic factors for the high I-values clearly decrease more rapidly than do those for the low I-values. The ratio of the I= 5 to 1= 0 spectroscopic factors at 35, 55 and 122 MeV are, for example, 4.06, 2.27 and 1.8, respectively. The decrease of spectroscopic factors for the higher l-values in the (p, d) reaction as the bombarding energy is increased has been previously observed for the 308Pb(p, d)*“Pb reaction 6*7) and the “Zr(p, d)*‘Zr reaction ‘). With the inclusion of the data from the present study the effect now seems well established, and it does not appear to depend strongly on the mass of the target. In reviewing the possible causes of the problem, the reaction mechanism will be discussed first. The question of whether the optical model parameters or the geometrical parameters for the bound state calculation are the cause of the problem has been explored previously 6,7). It was concluded that while changes in these parameters will effect the absolute values of the spectroscopic factors there was very little influence on the relative trends with energy if consistent sets of parameters are used. It has also been observed that at a particular energy the ratio of spectroscopic factors for two states is quite insensitive to the particular choice of parameters. It is known that while the adiabatic deuteron approximation tends partially to account for deuteron break-up effects a more complete treatment involves a full coupled-channel formulation of the three-body problem. Calculations have been

S.A. Dickey et al. / 54Fe, ‘@Ce($,

carried out using a procedure that such calculations

outlined

by Shepard,

do not account

d)

207

Rost and Kunz 27) which indicate

for the observed

energy-dependent

effects.

A comprehensive set of coupled-channel calculations for two-step processes has not been carried out for the case of 54Fe and i4’Ce. Previous calculations for “*Pb [ref. “)I and for ‘Li [ref. ‘“)I which involved a very collective set of inelastic transitions, indicate very strongly that if the (p, d) transition is a relatively strong single-particle transition that the two-step processes do not play an important role. It is also to be noted that as the projectile energy increases one would normally expect the two-step process to become more important, while what is observed is a decrease in the apparent spectroscopic strengths at least for higher I-values. It would seem unlikely that destructive interference between the one- and two-step processes would always be the case for all of the transitions that have been studied. The fact, that at higher energies the (p, d) amplitude is sensitive to high-momentum components of the deuteron and target wave functions, has led to an explanation of the energy dependence of the ratio of the 3+ state in 6Li to the l+ ground state cross sections with incident proton energies of 100 to 800 MeV [ref. ‘“)I. It is difficult to see, however, how similar mechanisms can play an important role for predominantly single-particles states excited with even-even targets such as 54Fe, 90Zr, 14’Ce and “‘Pb. In summary, analyzing-power data and cross sections have been measured for the (6, d) reaction on 54Fe and 14’Ce at an incident proton energy of 122 MeV. Since there were no previously reported analyzing-power data for either nuclide, unique spin assignments could be made for the first time to several states. The main purpose of the investigation, however, was to test whether the spectroscopic factors extracted from the (p, d) data taken on these targets for the strongly populated low-lying states at various energies were energy-independent. It appears from this analysis with exact-finite-range

DWBA

calculations

that the spectroscopic

factors

for the

higher I-values (3-5) tend to decrease by a factor of about 2 over the 25 to 122 MeV energy range, while for the lower I-values (O-l) they tend to increase by a factor of about two. These results are generally consistent with the earlier investigations of the 208Pb and “Zr(p, has been put forth.

d) reactions

6,7,5). No satisfactory

explanation

of these effects

References 1) 2) 3) 4) 5) 6) 7) 8) 9)

J.J. Kraushaar et al, Nucl. Phys. A394 (1983) 118 R.P. Liljestrand et al., Phys. Lett. 99B (1981) 311 G.R. Smith et al., to be published P.W.F. Alons et al., Phys. Lett. 145B (1984) 34 P.W.F. Alons, J.J. Kraushaar and P.D. Kunz, Phys. Lett. 137B (1984) 334 R.E. Anderson, J.J. Kraushaar, J.R. Shepard and J.R. Comfort, Nucl. Phys. A311 (1978) 93 S.A. Dickey, J.J. Kraushaar and M.A. Rumore, Nucl. Phys. A391 (1982) 413 V.C. Officer, R.S. Henderson and S.D. Svalbe, Bull. Am. Phys. Sot. 20 (1975) 1169 R.L. Auble, Nucl. Data Sheets 21 (1977) 323

208

S.A. Dickey et al. / 54Fe, ‘*OCe(& d)

10) L.K. Peker, Nucl. Data Sheets 32 (1981) 1

1I) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28)

P.D. Kunz, University of Colorado, unpublished F.D. Becchetti and G.W. Greenlees, Phys. Rev. 182 (1969) 1190 P. Schwandt ef al., Phys. Rev. C26 (1982) 55 R.C. Johnson and P.J.R. Soper, Phys. Rev. Cl (1970) 976 J.D. Harvey and R.C. Johnson, Phys. Rev. C3 (1971) 636 CD. Goodman, J.B. Ball and C.B. Fulmer, Phys. Rev. 127 (1962) 574 J.C. Legg and E. Rost, Phys. Rev. 134 (1964) B7S2 R. Sherr, B.F. Bayman, E. Rost, M.E. Rickey and C.G. Hoot, Phys. Rev. 139 (1965) B1272 S.A. Dickey, C.A. Fields, J.J. Kraushaar and M.A. Rumore, to be published R.O. Nelson, C.R. Gould, D.R. Tilley and N.R. Roberson, Nucl. Phys. A215 (1973) 541 T. Suehiro, J.E. Finck and J.A. Nolen Jr., Nucl. Phys. A313 (1979) 141 H. Ohnuma, T. Suehiro, Y. Ishizaki, J. Kokame, I. Nonaka, H. Ogata and Y. Saji, J. Phys. Sot Japan 32(1972)1466 C.M. Perey and F.G. Perey, Phys. Rev. 132 (1963) 755 A. Chaumeaux, G. Bruge, H. Faraggi and J. Picard, Nucl. Phys. Al64 (1971) 176 R.K. Jolly and E. Kashy, Phys. Rev. C4 (1971) 1398 K. Yagi, T. Ishimatsu, Y. Ishizaki and Y. Saji, NucI. Phys. A121 (1968) 161 J.R. Shepard, E. Rost and P.D. Kunz, Phys. Rev. C25 (1982) 1127 J.J. Kraushaar et al., to be published