Spectroscopy of 47K and proton core-excitations in 48Ca from the 48Ca(t, α)47K reaction

Nuclear Physics A465 (1987) 445-460 North-Hoiland, Amsterdam

SPECTROSCOPY

OF 47K AND

PROTON

CORE-EXCITATIONS

IN 4sCa

FROM THE ‘$%a(t, fx)*‘K REACTION

C.A. OGILVIE,

D. BARKER, J.B.A. ENGLAND, M.C. MANNION, L. ZYBERT’ and R. ZYBERT’

J.M. NELSON,

Received 28 October 1985 (Revised 14 July 1986) Abstraetr The =Ca(t, c~)~‘K reaction has been measured at 33 MeV bombarding energy. Spectroscopic information has been extracted for 13 states in 47K and 9 new levels have been observed in this nucleus. A comparison of spectroscopic factors is made with a recent shell-model calculation and the presence of proton core-excitations in the ground state of 48Ca is examined.

E

NUCLEAR

REACTIONS 48Ca(t, (Y), (t, t), (t, t’), E = 33 MeV, measured u( 6). 47Kdeduced levels, spectroscopic factors. Enriched target.

1. Introduction

&Ca is thought to be one of the better examples of a doubly magic nucleus. Therefore the single-proton pickup reaction probes two complementary aspects of nuclear structure: the mixing of single-hole configurations in the residual nucleus, and the possible presence of proton core-excitations in the ground state of the target. The proton single-hole configurations that are expected to be important in 47K are the (2s,,4-‘, ( ld3,J1 and the ( ld5,J-’ orbitals. It is known iY2)that the ground state of 47K has a spin and parity of $’ and exhausts a large amount of the (2s1,J1 strength. It is only recently 3, by the measurement of analysing powers in the 48Ca(& 3He)47K reaction that it has been possible to separate the contributions of the (ldj,J-’ and ( ld5f2)-1 configurations to the states of 47K. The most complete shell model study “) to date had very little expe~mental info~ation conceding the role of the (ldsjz)-’ configuration and for this reason the shell-model space was restricted to ( ld3,2)-1 and (2~~~~)~~proton configurations. Our experimental results are largely consistent with the spectroscopic information obtained by Banks et al. 3, and together they should provide a useful input for a shell model calculation that includes the ( ld5J1 configuration. ’ On leave from the Institute of Nuclear Physics, Cracow, Poland. ’ On leave from the Jagellonian University, Cracow, Poland. 03759474/87/%03.50 @ Eisevier Science Publishers (Noah-Holland Physics Pnbiishing Division)

B.V.

446

CA. Ogiluie et al. / 48Ca(t, CI)~‘K

A further result of the ““Ca(d, 3He)47K experiment was the reported presence of proton core-excitations in the ground state of 48Ca. This was based on the assignment of a direct I = 3 transfer to the 2.0 MeV state in 47K. However, the I = 3 calculation does not reproduce the measured cross section for angles beyond the first minimum and the possibility of two-step reaction mechanisms has not been considered. The presence of core-excitations in the ground state of 48Ca is often used to explain the experimentally observed suppression of the Ml transition strength 5,6) and the “missing” Gamov-Teller strength in the (p, n) reaction ‘). The detailed analysis of more complete angular distributions presented in this paper will be compared with the results of Banks et al. 3).

2. Experimental method and data reduction A 33 MeV tritium beam was provided by the Nuclear Structure Facility tandem accelerator at the Daresbury Laboratory, UK and was focussed onto a 362 pg/cm2 target of 48Ca enriched to 93%. Reaction products were detected by ten solid-state AE - E telescopes. Each telescope consisted of a 120 pm surface barrier silicon AE detector together with a 5 mm lithium drifted silicon E-detector. Four solid-state detectors were used to monitor the target. Signals from each telescope were hardware gated “) into energy spectra corresponding to different particle types, enabling simultaneous collection of p, d, t, 3He and LYspectra. Counting rates were kept below 2 kHz/telescope and the resulting dead time was less than 1%. Data were collected from 7.5” to 31.25” in 1.25” steps and from 32.5” to 125” in 2.5” steps. The horizontal acceptance for each telescope was 10.3”. Each run was no~alised using the integrated beam current measured in a suppressed Faraday cup. The target thickness was determined by a normalisation grid on the elastic data and searching for the optimum optical-model fit at forward angles. The total error of our absolute cross sections is estimated to be 10% and is mainly due to the uncertainty in the target thickness determination. This error is not included in the angular distributions shown in the following sections. The overall energy resolution obtained for cu-particles was 75 keV and a typical energy spectrum is shown in fig. 1. The Gauss fitting procedure GAFOR9) was used to extract peak areas from those parts of the energy spectrum where groups overlapped. An extended run was performed at larger angles to find the excitation energy of each weakly populated state. The criterion used to establish the existence of these states was that the constructed level scheme from each spectrum had to be independent of angle. The energy calibration of spectra at forward angles included 15N peaks originating from I60 in the target. This calibration provided the excitation energies of those 47K states strongly populated at forward angles. These 47K states were then used as calibration points for the backward angle spectra. Using this method we have deduced the existence and energies of a further nine levels in 47K.

C.A. Ogilvie et al. / 48Ca(t, ~Y)~‘K 800 COUNTS

%d3H,‘He)L7

z

8 1! 447

(D m d

K

600

6

8

m

ui

0) m

1100

co

\f

1150

1200

CHANNEL

125

d

1 3( 10

Fig. 1. A typical energy spectrum of outgoing alpha particles from the “sCa(t, a)47K reaction at W’(lab). The strongly populated 47K states are labelled in MeV and contaminants are marked with hashed lines.

Fig. 2 demonstrates peaks as a function

this method of angle.

by plotting

the excitation

energy

of the observed

3. Analysis of data The optical model parameters found by the search programme describing the t+56Ni scattering cannot

be well defined

without

for the t+48Ca elastic scattering at 33 MeV were RAROMP lo) using as starting parameters those at the same energy ‘l). The spin-orbit potential polarisation

measurements,

so a final search on its

geometrical parameters was performed at the end of the analysis whilst keeping the depth of the potential constant at 2.2 MeV. The experimental data and the corresponding fit are shown in fig. 3. The definitions of the potentials used, along with the final optical-model parameters are included in table 1. The extracted angular distributions from the 48Ca(t, CX)“~Kdata have been compared with those calculated by the full finite-range coupled-reaction channel code FRESCO 12> and the full finite-range DWBA code FRUCK2 13). The entrance channel optical potential used was that obtained from the above analysis of triton elastic scattering whilst the exit-channel potential has been chosen from analyses of alpha elastic scattering in this mass and energy region 14*15).The optical-model

C.A. Ogilvie et al. / 48Ca( t, CY)~~K

448

‘7K E

LEVELS

9 fX

( MeV)

_-__-

a P

-.-t--t

-.q--*--*_-.-**

~-___c~-_-_-._* *----_--*~__*_c_ *

_

-

-

--__-_*_-*

* c

*- -

-

-

-

-

_ ,_*-•-*-

3 z?:z *-.-~z~~

_rz_---~_-_-z_p

--_--------__

-

-4-*

1

a*-*

*--t-e-

-

--e-*9-o--C-e-***

-

--e---_-s--c~~-,-~ -*--.-_-_~_-_--

-

_-*_e_._.

t-

_

*)-*_

-----,-

f-

-

--•

e-q--_,

__I__

-

--~.-*-e-*-.

-

-~-o-*-o-*4-**-*

AMGLE

-a-*

__

i,

(LAB 1

Fig. 2. The measured excitation energy of 47K peaks in each alpha spectrum over a series of laboratory angles. The errors are smaller than the circles shown and the averaged excitation energy for each state is shown on the left as a solid line. A star indicates a newly observed level in “‘K.

parameters for both channels (as used in coupled-reaction channel and DWBA calculations) are included in table 1. For each finite-range transfer calculation, the form factors were generated in a Woods-Saxon potential using the well-depth procedure. Whilst this is not thought realistic for the (tie) overlap nor for the states of 47K with small spectroscopic factors, it is considered that sophisticated models are not wa~anted given the uncertainty in the bound state radius. We found that a 5% increase of this parameter (for the (48Ca)47K)overlap) increases the predicted cross section by 20%. The final values chosen for the bound state geometry are included in table 1.

449

C.A. Ogilvie et al. / 48Ca( t, ~x)~‘K %I(~H,~

I

1o-3 0

I

I

20

E =

H )“Ca

I

I1

40

I 60

8cm Fig. 3. The angular

3.1. DIRECT

distribution

and optical

I

33

I

I

80

100

MeV

I

I

I

120

I

I

140

(deg.)

model fit for the “sCa(t, t)“*Ca elastic 33 MeV.

scattering

at Elab =

TRANSITIONS

In the following sections DWBA prediction da/dL?bw

the measured by

cross section

da/d0

is related

to the

I

DW

where C denotes the isospin Clebsch-Gordan coefficient and Scnrij the spectroscopic factor for the pickup from an orbital nlj in 48Ca. 3.1.1. I=0 transfers. Two I=0 transfers were observed in this experiment. The first to the ground state of 47K and the extracted spectroscopic information is consistent with previous results lm3). Recently ‘) (2~i,J-~ strength has also been observed at 3.80 MeV and our results confirm this with a 1’ state at 3.85 MeV. Within the framework of our DWBA calculations (i.e. for an assumed bound state radius) these two states exhaust 90% of the available shell-model strength. The data and DWBA calculations for these two transitions are shown in fig. 4. 3.1.2, 1=2 transfers. Although many I= 2 transfers were observed in this experiment, our data has revealed no j-sensitivity. Therefore in order to differentiate we have relied on the between transfers from the Id,,, and Id,,, configurations work of Banks et al. ‘) who determined the j-value in the transfer by means of

C.A. Ogilvie et al. / 48Ca( t, CK)~‘K

450

TABLET Parameters used in DW calculations Optical potentials Entrance channel V, = 129.2 MeV r,=l.ll fm a, = 0.8 fm

W,,,,= 17.3 MeV r, = 1.32 fm a, = 0.73 fm

V, D = 2.2 MeV r, 0 = 1.03 fm a, o = 0.76 fm

Exit channel’4~‘s) V, = 183.7 MeV r,=1.4fm a, = 0.564 fm

W,,, = 30.3 MeV r, = 1.402 fm az = 0.564 fm

rot = 1.3 fm

where Woods-Saxon

r,, = 1.3 fm

f(r, a, R) radial shapes are used and df(r, a, R) V surf= 4aKurf dr

’

(R = roAq3) ,

Bound state parameters Woods-Saxon

geometry r, = 1.25 fm

a = 0.65 fm

and

A,,

= 18

where

I and i$, is the mass of the proton.

analysing power measurements. Our results are consistent with most of the Id,,, strength being in the first excited state at 0.36 MeV. Further Id,,, strength is seen at 3.93 MeV and these two states over exhaust the sum rule limit. There may be other reaction mechanisms populating one or both of these states, which (assuming constructive interference) would lower the required f 1d&-‘* spectroscopic factors. If we model the 47K$+state at 3.93 MeV as a linear combination YKp) = al(ld,,,)-‘)+

b148Ca2’O(2s,,2)-1)3,2+

then this state will be populated by the direct Id,,, pickup and also by two-step processes. Only the coupling to the (2s,,J1 is considered since this configuration lies closest to the Fermi surface. The indirect mechanisms are I = 2 inelastic excitation to the 3.83 MeV 2* state in 48Ca followed by the transfer of a 2s 1/2 proton, and the transfer from the ground state of 48Ca to the ground state of 47K followed by an I = 2 inelastic excitation in the exit channel. The data and the single-step (deduced p2 = 0.13) population of

CA. Ugil& et al. / AsCa(l, a147K ~6C~~3H,‘H~)‘7~

451

E =

33

MeV

%2

TRANSFER

0.0

‘\I\

MeV

9

3.85

MeV

lo@cm (deg

)

Fig. 4. The angular distributions for the %a(t, CW)‘%reaction leading to the ground state and 3.85 MeV state in 47K with the corresponding finite range DWBA calculations for the 2~,,~ proton pickup.

the 3.83 MeV 2+ state in 48Ca are shown in fig. 5. If it is assumed that the 48Ca 2+ is formed by exciting neutrons into higher ~on~gurations then the spectroscopic amplitude for the (48Ca 2t/47K$+) overlap can be approximated to be the same as the amplitude for the ground state to ground state transfer multiplied by the (2+0(2~,,~)-‘) component in the 47K4+ wavefunction. Likewise if we assume that the hole in the proton (sd) shell does not affect the inelastic coupling, then &(47K) = p2(48Ca) again multiplied by the same (2+0(2s,,,)-‘) component. Unfortunately there are no B(E2) measurements for 47K to test this assumption. The direct and indirect transitions were calculated in exact finite range I*) with the direct process being the dominant reaction mechanism. Even if lb/> /a/, the shape of the calculated distribution will be similar to that of the direct pickup. We have treated the magnitudes of the amplitudes as free parameters restrained by two conditions: (i) that the magnitude of the cross section be reproduced (assuming constructive interference between the direct and indirect processes); and

C. A. Ogiloie et al. / 48Ca( t, (Yj4’K

452

E=

“CC~(~H 3H’)~EC~

0

20

40

60

0crn

80

(deg

100

33 MeV

120

3.83

Me’4

4.507

Me’/

140

1

Fig. 5. The inelastic angular distriblttions from the %a(& t’)48Ca reaction for the 3.83 MeV 2+ and 4.507 MeV 3- states in “Ca, with single-step DWBA calculations

(ii) that la12+lb\2= 1. This resulted in the following values Ial = 0.35O,lbl= 0.937 implying a direct spectroscopic factor of C2S = 0.49 for the 3.93 MeV state. If the 0.36 MeV wavefunction is modelled as orthogonal to this wavefunction then its extracted spectroscopic factor remains very close to the previous value. The resulting sum of extracted spectroscopic factors is closer to the sum rule limit. Fig. 6 shows the data and calculated angular distributions for the z’ states. The Id,,, strength is fragmented amongst many states and our results are in very good agreement with Banks et al. ‘), The total strength measured exhausts two-thirds of the shell-model limit. Figs. 7a and 7b show the data and the DWBA calculations for the Id,,, transitions. 3.2. INDIRECT

TRANSITIONS

In the following two sections, the angular dist~butions of the states are not reproduced by direct transitions and hence contributing indirect mechanisms have been considered. 3.2.1. The 2.02MeV state. The existence (and extent) of proton ground state

CA.

Ogilvie et al. / 48Ca(t, LI)~‘K

%I(~H,‘H~)~~K

E =

33

453

MeV

MeV

MeV

@cm

(deg.)

Fig. 6. The same as fig. 4 but for the 0.36 MeV and 3.93 MeV states in 47K with a pickup

core-excitations

in 48Ca can be inferred

from the observed

pickup

of a Id,,,

proton.

of a lf7,* proton.

Banks el al. ‘) suggested that the state at 2.02 MeV in 47K exhibits features of an Z=3 transfer and the polarisation measurement is consistent with their J” =gassignment for this state. The more complete angular distribution for the 2.02 MeV level obtained in this experiment clearly indicates the presence of two-step processes in populating this state, as a pure 1= 3 transfer does not reproduce the data. Let us assume for the moment that this state has a spin and parity of g-. The two dominant indirect mechanisms will be inelastic excitation to the 4.507 MeV 3- state in 48Ca followed by the pickup of a 2s r12 proton, and the transfer from the ground state of 48Ca to the ground state of 47K followed by an 1= 3 inelastic excitation in the exit channel. The inelastic transition to the 4.507 MeV 3- state in 48Ca was fitted as a single-step transition with & =0.16. The experimental data and calculated angular distribution are shown in fig. 5. The spectroscopic amplitude for the transfer from the 48Ca 3- state can be found from the wavefunction overlap (48Ca, 3-14’K, $-). To calculate this overlap, the $- state can be modelled as a linear combination of two basis configurations: a (lf7,20(sd)-2) configuration and a (3- phononO (2s1J1) configuration. The wavefunction for the assumed i- state was calculated 16)

C.A. Ogilvie et al. / 48Ca(f, CY)~‘K

454

0

0

0

0

(JS/cwJ)

0

0 (J+VJJ)

UP/DP

-2 UP/.oP

0

0

7

0

C.A. Ogiloieet al. / “‘Ca ( t,

CY)~'K

455

within this two-state model using the results of ref. 17).The spectroscopic amplitude is then taken from the (3- phonon@(2s&-‘) component of this wavefunction. The exit channel two-step route was calculated in a similar fashion. The transfer to the ground state of 47K was fitted to the experimental data. Assuming weak coupling, the & appropriate for the 47K inelastic transition is &(“%a) multiplied by the amplitude of the (3- phononO(2s,,,)-‘) component in the calculated 47K $wavefunction. Both two-step reaction mechanisms were calculated in exact finiterange “) and were taken to coherently populate the 2.02 MeV state in 47K. However, the resulting calculation is a factor of ten smaller than the experimental distribution at forward angles. In order to fit the magnitude of the cross section, the direct pickup of lf,,* protons can be included and the strength required is a measure of the lf7,* proton occupation in the ground state of 48Ca. The shape of the forward angle data confirms the need for an I= 3 transfer. However, the magnitude of the spectroscopic amplitude is not uniquely determined by our data alone. If the direct process is assumed to interfere constructively with the two-step processes then the extracted value for C*S is 0.11, whereas the assumption of destructive interference results in an extracted value for C’S of 0.22. Both calculations fit the shape of the experimental dist~bution given the accuracy obtained in the present experiment. The angular distribution assuming destrnctive interference is shown in fig. 8. In an attempt to resolve this ambiguity the same nuclear structure considerations have been applied to the 48Ca(& 3He)47K data of Banks et al. ‘). With the & values and calculated 47Kwavefunctions as above both the (t, a) and (a, 3He) cross-sections are reproduced with the same If 7,2 spectroscopic factor of C2S = 0.22, if the direct transfer interferes destructively with the two-step processes. The lf,,* spectroscopic factor deduced from our data assuming constructive interference does not reproduce the (3, 3He) cross section. It is noted that both the above calculations reproduce the (d, 3He) vector analysing powers. Neither set ((t, a) and (3, 3He)) of experimental data are by themselves sufficiently accurate nor do they cover sufficient angular range to distinguish between the two interference possibilities. Taken together, they suggest that the direct and indirect processes destructively interfere. In order to underline the uncertainty in the spin and parity of the 2.02 MeV state one can make an alternative assumption on the structure for this state, namely

147W s12+ or 3/2+ =

14’Ca.

2+0(2~~&~~~~~+

d/2+

.

Such a state has no direct overlap with the ground state of 48Ca. Two 3.83 MeV 2+ state in 48Ca followed by the pickup of a 2s 1,2proton, and the transfer to the ground state of 47K followed by an I= 2 inelastic transition in the exit channel. The details and assumptions made in calculating the two indirect processes have been described in subsect. 3.1.2. The resulting angular distribution reproduces both the magnitude and the shape of the experimental data for the 2.02 MeV state (fig. 8) and the application of the same assumptions to the 48Ca(d, 3He)47K experiment 3, results in a satisfactory reproduction of the cross section. The analysing powers are consistent only with the coupling of the residual state to 2’.

456

CA. Ogilnie et ~2./ “Ca( f, CX)~‘K

E = 33

MeV

MeV

to+

’ 0

t

’

20

’

‘ 40

’

’

60

f3cm

’

’

80

’

’

100

’

’

120

’

’

140

(deg.)

Fig. 8. The angular distribution for the 2.02 MeV state in 47K. The full line represents the finite-range calculation for this state and includes two-step processes as described in the text plus direct pickup of a If,,, proton (~suming destructive interference). The dashed curve shows the finite-range calculation assuming the state to be a weakly coupled J” = 2’ level populated by two-step processes.

3.22. 7&e 3.72 MeV sfate. There are no spectroscopic indications as to the spin and parity of the 3.72 MeV state. In the present analysis we have not been able to fit the forward angle data with any direct I-transfer. To examine the possibility of two-step processes we followed the same procedures as outlined for the 2.02 MeV state. The angular distributions for both the $- assumption (using an orthogonal residual wavefun~ion) and the weak coupled p*Ca ~~O(~S~,J*)~,~+ or5,Z+assumption do not reproduce the shape of the experimental distribution (fig. 9). Therefore, it was not possible to assign a spin and parity for this state, nor deduce the mechanism of its population.

4. Discussion This work reports on the analysis of the 48Ca(t, a)47K reaction at 33 MeV. The high energy triton beam from the NSF in Daresbury has proved to be an excellent spectroscopic tool and has provided spectroscopic information for 13 states of 47K and evidence for the existence and excitation energies of a further 9 states. Our results compare well with those of previous studies r-3) and have extended the

457

C. A. Ogilvie et al. / @Ca( t, a Y”K ‘8Co(3H,‘Hef7K

loo

E

=

33 MeV

E

L < E U

t

10-L ’ 0

1

’

’ 20

’

’ 40

3.72

’ 0cm

I 60

I

n 80

t

’

100

’

I 120

MeV

’

’ I40

(deg.)

to the same Fig. 9. The angular distribution for the 3.72 MeV state in 47K . The two lines correspond calculations as described in fig. 8, with the exception that for the full line, the direct pickup is assumed to constructively interfere with the two-step processes.

analysis to include two-step processes and the influence these have on the extracted spectroscopic information. The most complete shell-model description of the potassium isotopes has been performed by Johnstone “) (1980). The effective interaction used in his calculations reproduces the changing importance of the 2s,,*, Id,,, hole configurations along the isotopic series. The effective particle-hole interaction is less repulsive for 2s,,, holes than that for Id,,,

holes and reproduces

the experimental

spin and parity

of

L+ for the ground state of 47K (the ground state of 39K is p). Table 2 compares the 2 spectroscopic results of this experiment with the shell model predictions “) and with a previous experiment ‘). Overall the agreement between our data and the calculations is good, the major disagreement being that the shell model underpredicts the strength of the second 5’ state at 3.93 MeV. As a further result, the combined work of this experiment and that of Banks et al. ‘) may provide enough spectroscopic information to place constraints on the particle-( ld&l interaction. There are two possible ansatzes for the spin and reaction mechanism leading to the 2.02 MeV state of 47K, making it impossible to distinguish between the assignment of s- or of $‘. This is also the case for the data of Banks et al. ‘). One possible structure for the 2.02 MeV state that does not require core breaking in the ground state of 48Ca, is the weak coupling wavefunction 14*Ca 2+0

C.A. Ogilvie et ~1. / 4sCa( t, CX)~‘K

458

TABLE 2 Levels of 4X Shell model “)

Our results

energy (MeV) 0.00*0.02 0.36 + 0.02 2.02 * 0.02 3.35*0.03* 3.46 f 0.03 3.72*0.02* 3.85 + 0.02 3.93 f 0.02 4 17*006** 4:36 k 0:04** 4.74 f 0.04** 4.90 f 0.04+* 5.24kO.2 5.49 f 0.02 5.79 f 0.02** 6.15*0.04* 5 26*004** 6:42 k 0:04** 6.51 i 0.03 6.87 f 0.04 7.15 f 0.05*+ 7.38*0.04** 7.57 f 0.03 7.81 kO.03 8.13=kO.O5

J”

$’ Z?+ :i f’

nlj

C%

energy

C2S

energy

J”

nfj

2s l/2 lds,z lf7,2

1.50 3.88

0.0 0.36

1.59 3.91

0.0 0.36

f+

2s 1/z ld,/r

1.55 4.16

ids,,

0.78

1+ 2 3+ 2

2%/Z lds,z

0.28 0.74 0.49 “)

If,/,

0.08

Id s/2 ld,,,

0.08 0.97

0.4

3.32 3.42 3.68 3.80

4”

2s l/Z

0.28

0.07

3.88

1”

1d,,,

0.70

ids,, ld,,

0.39 1.11

5.20 5.44

1” $”

ids/, ld,,

0.32 0.94

1.97

5.0 4.3

3 $-

c%

I-e p

0.22

5+ 2

5+ 2 g+

Previous experiment 3,

6.3

(4’, s+“,

0.04

a+ ;+

Id 512 ids,,

0.31 0.12

6.44 6.81

$+ f’

ids/, Ids/,

0.22 0.14

I+ :+ 2 I+ r

ld,,, Ids,, Id s/r

0.13 0.72 0.39

7.48 7.73 8.02

5+ 2 5+ 1 I+ ?.

‘Ids,, Id,/, ids,,

0.14 0.71 0.33

* No spectroscopic information has been found for these states. ** New states observed by this experiment. “) C’S determined by including two-step reaction mechanisms in this state’s population.

@s*,2)-‘)5,2+ - Previous calculations I*) examining the location of lACa 2+0(sd)-‘) strength in A-‘K nucIei (where A is even) have primarily studied the fragmentation of deep-hole configurations: in particular the ( ldS,J’ configuration. Since the 2s,fz subshell is located near the Fermi surface, it is possible that the (48Ca2+@(2sI12)-‘) strength is concentrated at low excitation in 47K. However, the analyses of protonpickup reactions on the Ca isotopes re3) have not included the study of two-step processes and it is therefore not possible to compare the predictions of the weakcoupling model with the experimental data along the A-chain. The other possibility is that the 2.02 MeV state has a spin of i-. The If,/, spectroscopic factor from the (48Ca, g,s./47K, z-) overlap is calculated r6) to be C’S = 0.18, and is in agreement with the C’S = 0.22 spectroscopic factor extracted

C.A. Ogilvie et al./ 48Ca(t, nj4’K

in this analysis. ground

It should

be mentioned

state given by this calculation

a 48Ca(& cu)4K experiment ation in the ground

that the proton 16) is n( If,,,)

r9) indicated

a proton

459

occupation

number

= 0.051. Recently occupancy

of

of the lfT12 configur-

state of 48Ca ten times larger than suggested

At this stage it is not clear why there is a discrepancy,

in 48Ca

the results

though

by this experiment. its resolution

may

lie in a careful analysis of the (d, C-X)reaction mechanism. The amount of core-excitation in the ground state plays an important role in the experimentally observed suppression of the Ml transition strength. A calculation 20) of the transition strength, using the amount of 2p-2h core-excitation inferred by Banks et al. 3), showed that this degree of freedom could not account for the experimental results. The spectroscopic factor extracted in this analysis however is approximately three times larger than given by Banks. There are indications 21) that zero-point phonon fluctuations in the ground state wavefunction can further reduce the calculated Ml strength. The extracted lf7,2 spectroscopic factor is dependent on the adequacy of the residual $- wavefunction, about which very little is known. More is known about the negative-parity states in other odd-A K-isotopes. The I = 3 transfer in stripping reactions on Ar 22,23)indicate that the lowest g- states in 39K and 41K are dominated by the ((sd)-20 If,,,) configuration with possible small admixtures of the (^Ca 3-O from the lowest (2s,,,)-‘) configuration. The measured 24-27) E3 and M2 transitions 41K and 43K have also indicated the need for only f- to the t’ ground state of 29K, a small component 28) originating from the phonon-coupled configuration. The previous analyses lm3) of proton pickup reactions on the even Ca isotopes to the negative-parity states in the odd K-isotopes have not included the possibility of two-step processes via the phonon-coupled configuration. Given the fact that the two-step mechanism can compete with the direct lf7,2 pickup, the deduced amount of core-excitation in the ground states of the Ca isotopes cannot be treated as final until realistic residual f- wavefunctions can be found and two-step processes included in the analysis.

The authors

are very grateful

for the contribution

of F. Barranco

towards

the

results of this paper. We also appreciate the encouragement given by and the various discussions held with Professors G.C. Morrison, H.T. Fortune and Dr. 0. Karban. One of the authors (CAO) acknowledges the Commonwealth Association of Universities for the provision of a scholarship, and two of the authors (DB and MCM) acknowledge the SERC for provision of research studentships and LZ and RZ for research grants. This work was performed as part of a set of tritium induced reactions and the authors would like to thank the technical crew of the Daresbury Laboratory and the help of collaborators from King’s College, London and the University of Bradford during data collection.

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