Properties of the low-lying negative parity states in 45Sc

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Submitted on 1 Jan 1976

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Properties of the low-lying negative parity states in 45Sc

Julien Chevallier, B. Haas, N. Schulz, M. Toulemonde

To cite this version:

PROPERTIES

OF THE

LOW-LYING

NEGATIVE PARITY

STATES

IN

45Sc

J.

CHEVALLIER,

B.

HAAS,

N. SCHULZ and M. TOULEMONDE Centre de Recherches Nucléaires et Université

Louis-Pasteur,

67037

_Strasbourg,

France

(Reçu

le 24 octobre 1975,

accepté

le 4 décembre

₁₉₇₅₎

Résumé. 2014 Les décroissances des états de

parité négative d’énergie d’excitation inférieure à 2 107 keV dans le noyau 45Sc ont _{été étudiées par la réaction}

_{42Ca(03B1, p03B3)45Sc}

à une _énergie de bombardement de 10,5 MeV. Les _protons ont été détectés dans un _compteur annulaire de silicium, à un _angle moyen de 171° par rapport à l’axe de faisceau. Des _spectres de _rayonnements 03B3 ont été

mesurés aux

_angles

105° ~ 03B8 ~ 0° au _{moyen d’un détecteur Ge(Li).} Les _spins et _{les vies moyennes des}

niveaux ainsi que les rapports d’embranchement et les _{mélanges multipolaires} des transitions 03B3

ont été déduits des mesures de corrélations _{angulaires proton-03B3.} Les éléments de matrice réduits des transitions

_{électromagnétiques}

ont _{été obtenus pour} un certain nombre de transitions. Des calculs

basés

sur le modèle à

_couplage

fort ont été effectués. Ces résultats sont compares a _{l’expérience.} Abstract. 2014 The

electromagnetic

decays of the _{negative parity} states in 45Sc up to an excitation energy of 2107 keV have been investigated via the

_42Ca(03B1,

_p03B3)45Sc

reaction at a

_bombarding

_energy of 10.5 MeV. Reaction _{produced protons} were detected in an annular silicon detector at an average

angle

of 171°. _Gamma-ray spectra were measured with a

_Ge(Li)

detector at

_angles

105° ~ 03B8 ~ 0°.

Spins

and lifetimes of the levels as well as

_branching

and

_mixing

ratios of their

_decay

03B3-rays have been obtained from proton-gamma angular correlation measurements. Reduced

_{electromagnetic}

tran-sition matrix elements have been extracted for a number of observed transitions. Calculations based on the _{strong coupling} model have been _performed. The results are _compared with experiment.

Classification

Physics Abstracts

4.440

1. Introduction. - The

low-lying negative parity

states in the 45Sc nucleus have been the

_subject

of several theoretical

_{investigations.}

Both the

_spherical

shell model of

_{McCullen, Bayman}

and Zamick

_[1]

who considered 5

_particles

coupled

in the

_lf7/2

shell,

and the

_{strong-coupling}

deformed rotator model of Malik and Scholz

_[2]

have been used in order to

explain

the

_{negative parity}

level scheme. However insufficient

_experimental

data were available to allow

a _very detailed test of these models.

The _energy levels and their

_decay

_properties

have been

_{investigated by}

_many authors. When this work

was

begun

the information available on the

45SC

nucleus had been obtained from the

_following

expe-riments : Coulomb excitation

_{[3-10], beta-decay [9],}

[11, 12],

radiative

_proton

_capture

_[13-16],

inelastic

proton

scattering [10], [17-21],

one or two

_particle

transfer reactions

_[22-25]

and the

_{(a, py)}

reac-tion

_[26,

_27].

The

_{low-lying negative parity}

states

from I’ =

_1/2-

to

_15/2-

have been

_extensively

discussed in all these _papers.

_However,

_many

ambi-guities concerning spin assignments

existed and the

electromagnetic properties

had

_scarcely

been

inves-tigated.

During

the course of the _present

_work,

Metzger

[28], using

the nuclear resonance fluorescence

technique,

deduced lifetimes for some excited states

in

_disagreement

with

_previous

values measured

_by

the

_Doppler

shift attenuation method.

_Finally,

some

high-spin

states have

_recently

been

_populated

in

heavy-ion

induced fusion

_evaporation

reactions

_[29].

In order to _get more information on the

_negative

parity

states _up to 2 107

keV,

lifetimes,

decay

modes and

_spin

values were measured

_using

the

42Ca(a,

_py)

45Sc

reaction. The

_{experimental procedure}

and data

analysis

will be

_presented

in section 2. The results of the _present work are

_given

in section 3. In the last

section,

the level scheme and the

_{electromagnetic}

properties

will be

_compared

to the results of a new

calculation in the framework of the _strong

_coupling

model.

Positive

_parity

states were also

populated

in this

reaction;

their

_properties

will be

_presented

and discussed in a _{separate paper}

_(M.

Toulemonde et

al.,

to be

_published).

2.

_{Experimental procedure}

and data

_analysis.

-2.1 EXPERIMENTAL PROCEDURE. - The excited states

of

45Sc

were

_{populated by}

the

42Ca(a,

py)45SC

304

tion at a

bombarding

_{energy of 10.5 MeV.} The

_doubly

ionized 4He

_particle

beam,

provided by

the 5.5 MV Van de Graaf accelerator of

_Strasbourg,

had an

intensity

of about 150 nA. The _target,

_positioned

at 45° to the beam

_axis,

consisted of a 150

_J,lg/cm2

metallic calcium film

_(enriched

to > 92

_%

in

_42Ca)

evaporated

on a 500

J,lg/cm2

metallic Ba

_backing

in order to _stop the

_recoiling

45 Sc

ions. This

backing

was

_deposited

on a thick tantalum foil which

_stopped

the beam. To _prevent the

_target

from

oxidation,

it was covered with a 100

Jlg/cm2

gold layer.

Protons from the reaction were detected in a

150

mm2

annular silicon counter

_placed

at 180° with

_respect

to the beam direction and 3.5 cm from

the

_target.

To eliminate the backscattered

_a-particles,

the detector was covered with an 25

mg/cm2

Al foil.

Under these

_conditions,

the _energy resolution of the

particle

detection _system was

_{approximately}

170 keV. A 80

_{cm3 Ge(Li)}

_counter, mounted on a movable

table at 6.5 cm from the

_target

_center, was used to

measure the _y-ray

_yield

at 0 =

0°,

35°, 55°,

900 and

1050 to the beam direction. The energy resolution of this detector was 3.5 keV for the 1.33 MeV

6°Co

y-rays. The instrumental

anisotropy

of the

arran-gement was determined

_{by measuring}

the

_angular

correlation of the

y-transitions

from the I’ =

_{1 /2 +,}

934.9 keV level in

45Sc.

The

_proton-y

coincidences were collected in a dual parameter system as described elsewhere

[30].

The

y-ray

spectra

were stored in 4 096 channels and the

proton spectra in 118. As an

_example,

the

_spectrum

of _y-rays, at 0 =

90°,

in coincidence with

protons

feeding

the 377 and 543 keV levels is

_presented

in

figure

1. It should be

_pointed

out that the

_difficulty

in the

_analysis

of the

_angular

correlation measurements

of Zuk et al.

_[26]

is removed in the

_present

case.

Because of the small _energy difference of the I’n =

7/2-,

ground

state and the 1n =

3/2+,

first excited _state

(12.4

keV),

the transitions

_desexciting

a level to both

FIG. 1. - Coincidence

Ge(Li) spectrum at 0 = 90° resulting

from the decay of the 377 and 543 keV levels in 45SC.

these states could not be resolved in the NaI detector. As can be seen in

_figure

_1,

such transitions are

_easily

analysed

in the _present

_experiment.

2.2 ANGULAR CORRELATION ANALYSIS. - Since

the

_outgoing

_protons were detected

_at

_{Op >}

=

171°,

magnetic

substates m = ±

1 /2

_were

populated.

Fol-lowing

the _arguments

_given

_by

Ball et al.

_{[31] ]}

for a

similar

_study

of the

_4°Ca(a,

_py)43Sc

_reaction,

the contribution from the m = ₊

3/2 substrates,

due _to

the finite size of the

_particle

_detector,

can be

_neglected

in this

_experiment.

The

_{experimental angular}

corre-lations for the

_strongest

transitions in

4sSc

_(an

example

is shown in the _upper

_part

of

figure

2)

were

fitted to a series of

_{Legendre polynomials.}

The coef-ficients of these

_polynomials

are listed in table I

while the

_branching

ratios extracted from them are

given

in table II. For the _very weak

_transitions,

these values

_(or

_limits)

were

_derived

from the 0 = 550 measurement. The allowed values of I and 6 are based

on

a x2

analysis

of the

_angular

correlations

_[32].

An

_example

of the

_X2

_plot

for two

_spin

_sequences for the 720.6 keV transition is shown in the lower _part of

FIG. 2. - Measured

angular correlation for the 720.6 keV

y-transition, along with the _{Legendre polynomial} fit _{(upper part)}

TABLE I

Results

_of

least _squares

_{Legendre polynomial}

_fits

to the _proton-y

_angular

correlations

figure

2.

_Spin

values were discarded if the

corres-ponding

X!in

was not within the 0.1

_%

confidence limit.

_Signs

of 6 are

_{given according}

to the

_phase

convention of Rose and Brink

_[33].

The errors

asso-ciated with 6 were obtained at

_{a x2}

value

_{corresponding}

to one standard deviation from

X;in.

In addition

possible spin

sequences and

mixing

ratios were

rejected

on the basis of

_unacceptable

transition

strengths

[34].

2. 3 LIFETIME ANALYSIS. - As

a check on

_possible

gain

shifts in the

Ge(Li)

system and in order to _get the energy

calibration, 56C0

y-rays coincident in the

Ge(Li)

counter and in a 5 x 5 cm

NaI(Tl) crystal,

shielded from the

beam,

were

_{simultaneously}

recorded. Peak

_positions

measured at the different

_angles

were

determined from first moment calculations. Each coincident y spectrum was calibrated and calibration errors were

quadratically

added to the errors found in the center of

_gravity

determination. The full

Doppler

shifts were

_computed

from the kinematics. The _average recoil

_velocity

of the

45Sc

ions was

p > = vie > ~

0.9

_%.

The

_experimental

atte-nuation factors

_F(i)

and the unshifted _y-ray

_energies

were

computed

from

_{least-squares}

fits to the expe-rimental

_points

versus cos 0

_(Fig.

_3).

The

_resulting

values are

_given

in table II.

The attenuation factor

_F(T)

was

_computed

as a

TABLE II

306

FIG. 3. - Attenuated

Doppler shifts for some _{y-transitions}

des-exciting negative parity states. The solid lines are least squares

fits to the measured _energies.

function of T with the

_{stopping theory}

of

_Lindhard,

Scharff and Schiott

_{[35] including}

the

_Blaugrund

approximation [36]. Recently

Broude et al.

_[37]

and Haas et ale

_[38]

have shown that lifetime values deduced from the

_{Doppler-shift}

attenuation method

_(DSAM)

can _vary

_depending

on the

_slowing-down

environ-ment. However the values obtained with calcium or

barium as the

_slowing

down material _agree with

those obtained in an

independent

_way,

namely

the

recoil distance method

_(RDM).

4°Ca

_being

a

conta-minant of the _present

_target,

the attenuated

_Doppler

shifts for the y-rays

desexciting

the 1 159 keV level in

_43SC,

_populated

via the

_40Ca(a,

_py)

_reaction,

were

analysed.

An

_experimental

attenuation factor

F(T)

= 0.12 _± 0.04 leads _to the

following

lifetime

T =

5.4 +28 ps

without

any correction to the

_stopping

power. A value T = 6.4 _± 1.5

ps has been determined

previously by

RDM

_[39].

The

_agreement

indicates

a correct

_{phenomenological}

treatment of the

_stopping

power for

45Sc

ions

recoiling

in calcium and barium.

Therefore,

no correction factors

_fn

and

_fe

were

applied

to the nucleon and electronic

_stopping

_powers. Limits

_assigned

to the mean lives were obtained

assuming 20 % uncertainty

in the

_stopping

_powers. The

_present

lifetime values as well as

_previous

results are

_presented

in table II.

3. Results. - A

summary of the

experimental

results obtained in the _present work and a

comparison

with

_previous

data are

_given

in tables II and III.

The over-all

_agreement

between the

present

lifetime

TABLE III

Spin

and

_multipole

_mixing

ratio values

_{derived from}

the _present

_angular

correlation measurements.

_Lifetime

and other _arguments

_limiting

In and 6 values are included

(see text).

values and those obtained in the resonance fluores-cence

_experiments

is

_good.

It should be

_pointed

out that our

reported

lifetime values for the 1 237 and

1409 keV levels are in

_disagreement

with the values

determined

via the

_{(p, p’ y)}

and

_(p,

_y)

reactions

respectively.

This difference _may come from the

treatment of the

_stopping

_power in the case of

recoiling

ions with lower velocities

_{(( B ) =}

0.4

_%

for the first

_reaction,

_{p > ~}

0.1

_%

for the second

one).

Furthermore since the 1 237 keV transition is pure

E2,

additional lifetime information is

_directly

available from Coulomb excitation

experiments

[3-10] ;

the

_weighted

_average of the

_reported

reduced E2 transition

_{probabilities, B(E2) f== 138±28}

e 2

fm4,

corresponds

to a lifetime

_{r==3 100+600}

_fs,

in

agree-ment with the _{present determined} value. As

_pointed

out

_earlier,

calcium and barium seem to be

_slowing

down materials

_providing

correct lifetime values

_using

the

_Doppler

shift attenuation

method;

this leads to a

greater confidence in the

_experimental

transition

probabilities

determined in the

_present

work.

Another

_general

remark concerns the

dipole

to

quadrupole mixing

ratios 6. The wide allowed _range

for 6

_resulting

from a

_{previous experiment [26],}

is now

_considerably

narrowed and can lead to much

more accurate values for the

_{B(E2) !}

reduced transi-tion

_{probabilities.}

Furthermore

_{unambiguous spin}

assignments

have been made for most of the

_negative

parity

states _up to 2 107 keV.

In this

_section,

some observed states of

4SSC

will be discussed

_{individually.}

Since no new information was obtained for the

3/2 -,

376.8

keV,

the

_{11 /2 -,}

1 237.5 keV and the

_15/2-,

2 106.8 keV

_levels,

_except lifetimes

(or

limits), they

will not be discussed

indi-vidually

here. The

_present

_angular

correlation and lifetime results confirm the

_spin

and

_parity

assign-ments made in reference

[22]

for the first

level,

in references

_{[26, 27]}

for the second level and in

3.1 720.6 keV LEVEL. - This level

decays

by

a

96.5

_%

branch to the

_7/2-

_ground

state and a 3.5

_%

branch not

_{reported previously}

to the

_3/2+,

12.4 keV

state. This level has been seen in the

_(3He,

_d)

reac-tion

_[22]

where the deuteron

_angular

distribution was

fitted with

_lp

= 3

implying I’ = 5/2 -, 7/2 - .

The

angular

correlation of the 721 keV transition leads to a definite I’ =

5 j2-

assignment (Fig.

2)

in _agreement

with Eastham and

_Phillips

_[10].

In order to

_reproduce

acceptable

E2 transition

_strengths,

6 values > 15 and

- 60 were

_rejected

and the value

_given

in table III

adopted. Taking

into account the

_weighted

_average value

_{B(E2) T}

= 67 ± 10

e2 fm’

deduced from

Cou-lomb excitation

_experiments

_[3-10]

and the

_branching

ratio and lifetime

values,

we calculate an absolute

value for the

_mixing

_{ratio 16}

₁

= 0.084 ± 0.007 in

excellent _agreement with the _present one.

3.2 1 068.6 keV LEVEL. - In both

stripping

and

pick

up reactions

[22, 23]

this state is

_populated

_by

an

lp =1

transition,

allowing I" =1 /2 -

and

_{3 /2 - .}

The level

_{decays by}

a

76%

branch to the

_3/2-,

376.8 keV level and a

24%

branch to the

_5/2-,

720.6 keV

_level;

this last branch was not

_{reported by}

Zuk et al.

_[26]

who could not resolve the 1068.6 --> 720.6 keV and 376.8 --> 12.4 keV transitions due to the use of an

NaI detector. In the _present case, the simultaneous

analysis

of the two

_reported

transitions rules out

I =

1/2

and

yields

_a definite In =

3/2-

_to the level.

This confirms the

_proposed

I =

3/2

value of Rust et al.

_[21]

based on the

analysis

of the

45Sc(p,

p’)

reaction in terms of Hauser-Feshbach

_theory.

3.3 1 409.5 keV LEVEL. - This level

was found

to

_{decay by}

a 87

_%

branch to the

_{7/,2- ground}

state

and

_by

a 13

_%

branch to the

_5/2-,

720.6 keV

_level,

in _agreement with the results of Blasi et al.

_[9]

_using

the

_45Sc(p,

_{p’ y)}

reaction. The last branch was not

observed in other

_experiments.

A _very weak branch

to the

_{3/2 -,}

376.8 keV level has been

_{reported by}

Chasman et al.

_[18]

and Rust et al.

_[21].

This weak transition could not be observed in the _present expe-riment.

The

_{negative parity}

for this level results from the

assigned

_L.p

= 0 + 2 orbital

_angular

momentum to

the transferred _{neutron-proton}

_pair

in the

_43Ca(3He,

_p)

reaction

[24].

The

_angular

correlation for the 1 409.5 keV transition can be fitted at the

_{0.1 %}

confidence level

by

I =

5/2,

7/2

and

9/2.

The

present

data alone are not sufficient to

_distinguish

between the different

_spin

_sequences. The

_{assignment 9/2}

-has been

_{proposed by}

Blasi et al.

_[9].

In that case,

the

_mixing

ratio for the

_ground

state transition would be 6 = - 0.44 _± 0.07.

However,

taking

into _account

the lifetime value

_given

in table II and

_considering

the weak branch to the

_{3/2 -,}

376.8 keV

_level,

the

_9/2

-possibility

can be ruled out on the basis of unrealistic

M3 enhancement.

_Moreover,

Rust et al.

_[21]

analys-ing

the

_experimental

_proton

_angular

distribution in terms of the Hauser-Feshbach

_theory,

_assigned

a

probable 7/2 spin

to this level. 3.4 1557.1 keV LEVEL. -

Only

a branch to the

3 j2-,

1 068.6 keV state has been observed in the

present work. In view of the limits set on other

_possible

branches,

it is in

_disagreement

with the results of Chasman et al.

_[18]

but does not contradict the

y-decay

proposed

by

Schulte et al.

_[14]

for this level. This state is

_{populated by}

an

_lp

= 1 transition in

both

_stripping

and

_pick

_up reactions

_[22,

_23]

which

implies

a

_{spin assignment}

of

112 -

or

_{3/2 - .}

In the

present

experiment

the

_angular

correlations for the 489 keV transition is consistent with

_isotropy

and thus with a

1/2 assignment

but can also be fitted

supposing

a

_{spin 3/2}

for the initial state. Our data alone are not sufficient to

_give

a definite

_spin

assign-ment.

_However,

_according

to Rust et al.

_[21],

the

experimental

cross section for this level in the

45Sc(p,

p’)

reaction

_gives

clear evidence that the

_spin

of the states is

_1/2.

3.5 1 662.0 keV LEVEL. - This level

appears to

decay

79

_%

to the

_7/2-

_ground

state and

_{21 %}

to the

11/2-,

1 237.5 keV level. The latter transition has not

been

_{reported by}

Sawa et al.

_{[27] using}

the same

reaction but at

_{higher bombarding energies.}

The

analysis

of the _y-ray

_angular

correlation for the 1 662.0 keV transition leads to I =

_5/2

or

_9/2.

Realistic

transition

_strengths

for the _present observed 1662.0 --> 1 237.5 keV transition are obtained

_only

for a

_{spin 9/2}

_assignment.

In

addition,

positive parity

can be

rejected

on the basis of unrealistic enhancement

for an M2

_component

in the 1 662.0 keV transition.

As a

result,

there is

only

one solution left : 1ft =

9/2-.

It should be

_pointed

out that the

_present

spin-parity assignment

as well as the d value for the

1 662.0 keV transition are in _agreement with the

quoted

values of Sawa et al.

_[27]

based on

angular

distributions and excitation functions.

3 . 6 2 092.3 keV LEVEL. - This level

was observed

in the

_43Ca(3He,

_p)

reaction with an

_Lop

= 0 ₊ 2

orbi-tal

_angular

momentum transfer

_[24].

It

_implies

nega-tive

_parity

for the state. The _present

_angular

corre-lation measurement for the

_ground

state transition

can be fitted at the 0.1

_%

confidence level

_by

I =

7/2

with 6 = 0.51 ±

0.10,

or I =

5/2

with 6 = 0.05 _± 0.06

and 6

_{5.7 12.1,}

or I =

3/2

with 6 = - 0.19 ± 0.12.

The

_angular

correlation for the 2 092.3 -+ 1 068.6 keV

(3/2-)

transition

_yields

the

_following

solutions : I =

7/2

with 6 =

0.21-0.17,

_or I =

5/2

with

6 = 0.05 _± 0.20 and 6 =

2.3 ± i : o

_or I =

3/2

with

6 0.24. On the basis of the lifetime results

presented

in table

_II,

the 1ft =

3 j2-

and 1ft =

7/2-

possibilities

can be

rejected

because

they

would

imply

an enhanced

M3 _component in the first and second transition

308

Since the

_positive

_parity

has

_already

been

excluded,

we are left with an

_{unique 5/2- assignment}

for the

spin

and

_parity

_{of this state ; the}

_{larger 6}

values are not

_given

in table III because

_they

lead to E2

enhan-cements _greater than 100 W.u.

4. Discussion. - Natural

parity

states for the

45SC nucleus have been calculated

_by

_McCullen,

Bayman

and Zamick

_[1]

in the framework of the

spherical

shell

_{model, considering}

5

_{particles coupled}

in the

_{If 7/2}

shell. The effective matrix elements of the residual interaction were estimated on the basis of

the

42Sc

level scheme as it was known at that time. New calculations have been

_performed

_{[29], [40]}

with

_improved

values for the residual interactions. A

_rough

_agreement has been found between the

energies

of the lowest levels with I >

7/2

and the calculated values. The measured excitation

energies

for the I =

3/2, 5/2, 1/2

levels _are

definitely

smaller than the calculated values and

_they

appear difficult

to reconcile with a _pure

(lf7/2)5

_{configuration}

for any reasonable set of matrix elements for the residual interaction

_[29].

This situation is not

_surprising

since the

3/2-states at 377 and 1 069 keV as well as the

_{1 /2 -}

state at 1 557 keV contain

_p-shell

admixture in their wave

functions as is shown in

_stripping

reactions

_[22].

An extension of the shell model

_basis,

to include the _p3/2,

_f5/2

and _P1/2 subshells has been

_attempted

recently by McGrory

[41]

but the calculations were

limited to nuclei with A 44.

_Figure

4 shows the

experimentally

established

_{negative parity}

levels _up

to about 2.2 MeV of

_43Sc,

45Sc

and 17 Sc. The data

on

43Sc

were obtained from reference

_[42],

those

on

45Sc

from the _present work and those on

47SC

from reference

_[43].

On the left side of the

_figure

are

the results of the shell model calculations

_[41]

for

(fP)’T=1/2

states. An

_improvement

in the calculation of the excitation

_energies

is observed as

_compared

with the _pure

_{(lf7/2 )3}

model.

_However,

the

_complete

low-lying odd-parity

spectrum cannot be understood.

FIG. 4. -

Low-lying negative parity levels of the nuclei _43Sc,

45 Sc and 47SC as _{presently known. On the left side of the figure}

are the results of shell-model calculations _[42] for

_(fp)3

states.

In the case of the odd scandium

_isotopes,

the

3/2+

states observed at _{very low excitation energy,}

strong-ly populated

by

_lp

= 2 transitions in

pick

_up

reac-tions

_[44],

are

_interpreted

as _proton holes in the

_d3i2

shell.

_43SC,

45Sc and 47SC

_display

_3/2+

levels at

_151,

12 and 767 keV

_{respectively.}

Such

_low-lying

_positive

parity

states _suggest that

_{configurations involving}

particle

excitations of the

4°Ca

core can be rather

important

for

_negative

_parity

states as well. In the model of Johnstone

_[45]

and Johnstone and

_Payne

_[46],

the

_negative

_parity

states of

43Sc

are assumed to arise from the mixture of _pure

_(fp)3

and

_5p-2h

_(five

particle-two

_hole)

K1C =

_{3/2 ‘}

rotational band states. An indication of the

_mixing

of the two _types of

configu-rations is

_{provided by}

the results of both the

_charge

exchange

reaction

_43Ca(3He,

_t)43Sc

_[47]

and _y-ray

spectroscopy

in

43SC

_[48].

This model can account for the observed

_{normal-parity}

level scheme.

_Although

similar

_{calculations,}

_involving

_(fp)5

and

_7p-2h

states

have not _yet been

_attempted

for

_45Sc,

we _{may compare}

the

_experimental

and theoretical results of

41SC

with the _present results of

4’Sc.

The

_strong

_similarity

between the level schemes of these two nuclei _suggest

a K1C =

3/2-

band in

45Sc

which

comprise

the levels

at 377 keV

_(3/2-),

721 keV

_(5/2-),

1 409 keV

_(7/2-‘)

and

_probably

the level at 1 662 keV

_(9/2-)

in addition

to states

_{arising chiefly}

from the

_{(fp) 5}

_{configuration.}

On the other hand the level scheme of

4’ Sc

differs

appreciably

from those of

43Sc

and

_{45Sc. However,}

in that case the _energy

_separation

of the first

3/2 +

core

excited state and the

_ground

state is

_larger

than in the other two

_isotopes.

Furthermore the _agreement between the _sequence of

_{low-lying negative parity}

levels and the

_(lf7/2)

calculations

_{performed by}

Brut

_[41]

is

_quite

_good.

This _suggests that the contri-bution of the two hole states is less

_important

than in

43Sc

and

45SC

due to the neutron excess.

Another

_approach

to the theoretical

_{understanding}

of

45Sc

is

_{provided by}

the _strong

_coupling

model of Bohr and Mottelson

_[49]

which has been

_reasonably

successfully applied

to various nuclei in the

_{If 7/2}

shell in

_spite

of its _great

_simplicity

_{[2], [50, 51].}

The calculations of Malik and Scholz

_[2]

for the

45Sc

nucleus show a better

_agreement

with the

experi-mental data than the

_simple

_(lf7/2)5

shell model.

Unfortunately

no transition

_{probabilities}

have been

calculated,

therefore a detailed

_comparison

with

experiment

is not

_possible.

Calculations

performed

in the present

study

are based on the same model. The Nilsson Hamiltonian was used to describe the

single particle

motion. The lowest intrinsic state in

45SC

is described with four neutrons

_coupled

to K = 0

in the Nilsson orbitals No. 14

_(K

=

1 /2)

and No. 13

(K

=

3/2)

and the odd

proton in the orbital No. 14

(K

=

1/2).

This

unpaired

proton was allowed to

occupy any orbit in the N = 3 oscillator shell. The

ground

state band has therefore K =

1/2

but,

due _to

model as well as

_explicit

relations for the matrix

elements are

_given

in reference

_[52].

The _parameters C and D used in the Nilsson Hamiltonian are

_equal

to - 1.77 and - 0.133

_[51]

consistant with the

_single

particle

energies

as deduced from 41SC and

49SC.

The value of the deformation parameter 6 =

0.14,

close to the minimum of the total

_ground

state _energy,

and the rotational constant

_h2l2

J = 90 keV

give

the best fit between the calculated and observed

spectrum. In

_figure

5 the

_{experimental negative}

parity

level scheme is

_compared

to the calculated one.

All levels are

_given

in the theoretical _{spectrum up} to 2.2 MeV and

_only

states with I >

_13/2

are

_reported

at

_higher

excitation _energy.

_{Electromagnetic}

pro-perties

were also calculated and the results of the

calculations are

_given

_along

with the

_experimental

values in table IV. The free nucleon

_charge

and

gyromagnetic

ratios were

used,

while a value of

Z/A

was

_adopted

for the rotational

_gyromagnetic

ratio.

Values of - 0.21 b and 5.36 n.m. are obtained for the

electric

_quadrupole

and

_{magnetic dipole}

moments

of the

_ground

state which have to be

_compared

to the

experimental

values

_[53]

of - 0.22 ± 0.01 b and 4.756 33 ₊ 0.000 01 n.m.

A _survey of both

_figure

5 and table IV leads to two statements. First of

_all,

a definite

_improvement

is

obtained for the _{energy spectrum : up} to 2.2 MeV excitation _energy, the model accounts for all the

negative parity

levels. On the other

hand,

several calculated transition

probabilities disagree

with the

experimental

data. At this

_point,

it should be reminded that for several other nuclei of the

_lf7/2

shell,

the

present model

_successfully

_reproduced

the

electro-magnetic

properties

for states

_having

a

predominant

ground

state

_{configuration [51].}

This fact _appears also in the _present

_{investigation}

where the main contri-bution to the wave functions of the first

7/2-, 3/2-,

11 /2-

and

_{1 /2-}

states

_corresponds

to the

_unperturbed

FIG. 5. -

Comparison of the calculated _{negative parity energy} levels in the framework of the strong coupling model (SCM) with

experiment. The levels of _angular momentum I > _15/2 are from reference _[29].

K1C =

1/2-

ground

_state band. The difficulties

encoun-tered for

_reproducing

transition

_{probabilities}

for other levels _may arise from the omission of other

_types

of excitation.

Thus,

the model

explicitly

treats the excitations of the

_unpaired

_proton from the Nilsson orbital No. 14 to all the other orbitals of the

_(fp)

shell

TABLE IV

310

but not the core excitations. Such excitations should

be

_implicitly

taken

into

account in a

phenomeno-logical

way and this may

explain

the fair agreement

obtained for the energy spectrum.

However,

the Note added in

_{proof :}

transition

_{probabilities}

are much more sensitive to

the details of the wave function. A better _agreement

for the

_{electromagnetic properties}

_may be obtained

taking

into account

_explicitly

the

_7p-2h

_component.

A value of

₍₃₀

_±

₃₎

_ps has been measured for the mean life the 2 107 keV level

_by

_Bini,

Blasi and Kutschera

(private

communication),

resulting

in a

B(E2) J,

value of 55 _± 5

e2

fm4.

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