Lifetime measurement of the first excited state in 22Ne

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Lifetime measurement of the first excited state in 22Ne

H. Sztark, J.L. Quebert, P. Gil, L. Marquez

To cite this version:

H. Sztark, J.L. Quebert, P. Gil, L. Marquez. Lifetime measurement of the first excited state in 22Ne.

Journal de Physique, 1972, 33 (10), pp.841-845. �10.1051/jphys:019720033010084100�. �jpa-00207314�

LIFETIME MEASUREMENT OF THE FIRST EXCITED STATE IN 22Ne

H.

SZTARK,

^{J. L.}

QUEBERT,

^{P. GIL and L.}

MARQUEZ

Centre d’Etudes Nucléaires de

Bordeaux-Gradignan, ^IN2P3,

Le

Haut-Vigneau, 33-Gradignan (Reçu

^{le 20 mars}

1972,

révisé le 2

juin 1972)

Résumé. ²⁰¹⁴ La vie moyenne du

premier

état excité de 22Ne

(2+,

1,277

MeV)

^a été mesurée _par la méthode du _parcours de

recul,

^à l’aide de la réaction

19F(03B1, p03B3)22Ne

^{à basse}

énergie :

^les rayonne- ments 03B3 ont été détectés en coïncidence avec les protons émis à 170° du faisceau incident. La vie moyenne trouvée est : ^{03C4 =}

(5,9 ± 0,6)

ps.

Abstract. ²⁰¹⁴ The mean lifetime of the first excited state of 22Ne

(2+,

1,277

MeV)

^{has been mea-}

sured

by

^the recoil distance

Döppler-shift method, using

the reaction

19F(03B1,

p03B3)22Ne ^{at low} energy.

The _03B3-rays were recorded in coincidence with the protons ^{emitted at 170° to} the incident beam.

The mean lifetime was determined to be : 03C4 ⁼

(5.9 ±

0.6) ps.

Classification : Physics ^Abstracts 12.00, 12.13, 12.20

1. Introduction. ^-

Among

the nuclear informations that can be deduced from

experiment,

^{the lifetimes}

of the excited states are

directly

connected with nuclear models

by

^{means of the reduced transition}

probabilities.

^{In the}

region

^between

^10-10

^and

10-12

_s, the «recoil-shift méthode

[1], [2], [3]

^is

the

only

^one which has

proved

^{to be}

sufhciently

accurate.

Indeed, by

^{this method the} average recoil

velocity

^{can be}

accurately

^known

by measuring

^the

energy difference between the _y-rays emitted

by

^recoil-

ing

^and

stopped

^nuclei.

We

adjusted

^this

technique

^{to very low}

energies

with 2.9 and 4 MeV

a-particles

^as

projectiles,

^{and we}

applied

^{it to} the 1.27 MeV state of

22Ne :

the mean

lifetime enables us to calculate the

B(E2, ^{0+ -} 2+)

of the 1.27 MeV

level,

^{that we have}

compared

^with

previous

^{results on}

quadrupole

^moments,

using

^the

rotational model.

II.

Expérimental

^{method. - The}

experiments

^have

been

performed

^at the 4 MeV Van de Graaff from the CEN de

Bordeaux-Gradignan.

^{Because of the}

low incident _energy, we had to choose an

exoergic

reaction to

get

^{a recoil}

speed

^{sufhcient for the studied}

nucleus. We used the reaction

19F(a, p) 22 Ne,

^whose

Q-value

^{is 1.698}

MeV,

^{at two incident}

energies :

2.9 and 4

MeV,

^{with a} beam of about 50 nA

intensity.

The thin

targets

^of

F2Ba (30 Jlg/cm2)

^were

evaporated

onto a copper foil 1 gm thick : this was then stretched

to

get

^{a surface as} flat as

possible.

The

recoiling

^{nuclei were}

stopped by

^{a brass}

plun-

ger, movable with

regard

^{to the}

target,

^{the surface} of which was

thoroughly parallel

^{to the stretched}

target :

the distance d between

target

^and

plunger

is

determined by measuring

^the

capacitance

^between

these two

surfaces,

^{and was known with an} accuracy of ± 1.5 _gm.

The _y-rays emitted

by

^the

recoiling

^{nuclei were}

recorded

by

^{a 60}

^cm’ Ge(Li)

^{coaxial detector at 0°}

to the beam : this detector has a resolution of 2.5 keV for the 1.27 MeV

22Na

line.

To

get

^a

good separation

^{of the two}

y-lines

^{and a}

good

definition for the recoil

velocity,

^{the y-rays were}

recorded in coincidence with the backscattered

protons

associated with the

recoiling

nuclei. These

protons

are detected with a surface barrier

ring-counter,

^at

180° to the incident beam : to

stop

^the

a-particles

diffused

elastically

^{at 1800}

by

^{the brass}

plunger,

^we

put

^{a 20} gm aluminium foil in front of the

ring-

counter, the thickness ^of which was calculated to

stop

^{the diffused} beam and let go

through

^{the back-}

scattered

protons.

The size of the detector defines the directions of the recorded

particles,

^{and then}

those of the

recoiling

^{nuclei taken into account :}

so, the recoil

velocity

^is very well established. More-

over the coincidence

circuit,

^{of the} multidimensional

kind,

^{allows us to choose a well defined} energy group of

protons,

^and

then,

^the y-rays

coming

^{from the}

decay

^{of a well} defined level

(the

^{first of}

^{22 Ne}

^{in our}

case) :

so, ^{we can} avoid

possible feeding

^{of the studied}

level

by

^a

decay

^of

higher

^states.

On

figure 1,

^{one can see the} difference between direct

spectra

^{for distances d = 6 and 30} gm, and the same

spectra

ⁱⁿ coincidence with

protons :

we can see the

advantage

^{of this last method in} the definition of the two

y-lines.

From the energy difference AE between the two lines of the coincidence

spectra,

^{we can} determine

accuratly

^the

recoiling

^nuclei

velocity

^v,

after correction for the effective solid

angle

^{at the.}

Ge(Li)

^detector

[3].

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:019720033010084100

842

FIG. 1. ^- Comparison between direct and coincidence y spectra.

Coincidences are obtained with protons ^{emitted at 170° to the} incident beam, ^{at 2.9 MeV incident} energy.

In our

experiment,

the direction of the

recoiling

nucleus is _very well known and no other corrections

are needed. On the

contrary,

^{if we want to evaluate} this

velocity

from the direct

spectra

^{we have to consi-} der other

corrections,

^{as described in reference}

[1].

We obtained the effective

values, for fi

⁼

v/c :

III. Results and

interprétation.

^-1. EXPERIMENTAL

DATA. ^-

Figure

^{2 shows some of the}

spectra

^obtain- ed in coincidence with

protons,

^{as a} function of the

stopping ^distance,

for 4 MeV incident energy. The variations in the relative intensities of the shifted and unshifted

peaks

^{can be}

clearly

^{seen : all}

spectra

^were normalised to

keep

^{a same total surface.}

The same

experiment

^{was made with a 2.9 MeV}

incident _energy.

For each

distance d,

^we calculated the surfaces u

and s of the two

y-lines

^after

subtracting

^{the back-}

ground,

^{evaluated on the most distant}

spectrum (d

^{= 79.4 pm at 4}

MeV).

In this kind of measurement, ^{it is} necessary ^to make

a number of corrections ^as described in reference

[3].

Many

of these corrections are

negligible

^{in our case ;}

for

instance,

all corrections due to the variations of solid

angles

^are very

small,

because of the _very short distances involved. In the same way, the variation in the ^counter

einciency

^for the shifted

peak

^leads

to an increase of

0.7 %

in the shifted

peak intensity.

The most

important

correction is due to the varia- tion of the

angular

distribution of the y-rays emitted

FIG. 2. _{- y} spectra ⁱⁿ coincidence with protons ^{emitted at} 170° to the incident beam, for distances d between 9.4 and 79.4 pm. These spectra ^{come from a 4 MeV incident} energy.

All the spectra ^were normalised on the spectrum corresponding

to the higher ^statistic (d ^{= 23.2} pm) ^to keep ^{the same total} surface (Iu + Is).

by

^the

recoiling

nuclei. We measured the

angular

distribution of the _y-rays emitted

by

^the

stopped nuclei, by using

^{a thick}

F2Ba target to stop

the recoil-

ing

^nuclei.

Figure

^{3 shows the}

experimental

^results

fitted with an

expression

of the form :

where

Q2

^and

Q4

^are the finite

geometry

^correction factors.

The

angular

distribution of _y-rays emitted

by

^the

recoiling

^{nuclei is modified and can be}

written,

^{at 0° :}

with

This leads to a decrease in the shifted

peak

^inten-

sity

^{of 1.5}

%.

FIG. 3. ^- Angular distribution of _y-rays in coincidence with protons ^{emitted at 170° to} the incident beam.

e experimental points normalised by ^the particle spectrum.

- theoretical curve : W(O) ⁼ 1 + a2 P2 (cos 0) + a4 P4(cos 0).

2)

INTERPRETATION. ^- We assume that the

2’

level can

only

^{be fed}

by

^direct excitation. This is the

case for the reaction studied because the

feeding by higher

^{states is}

rejected by

the coincidence method.

The

decay

^{law is :}

We then have :

where T is the time of

flight corresponding

^{to the}

distance d : T ⁼

d/v.

If we assume no

dependance

in time for the

angular

distribution of the _y-rays, we have :

which

gives :

In

fact,

^{a nucleus}

recoiling

^{in vacuum is}

subject

to the field of its electrons which modifies the

angular

distribution of the emitted _y-rays. To take this effect into

account,

^{we used the}

expressions given by

^Ben

Zvi et al.

[4],

^{and the} values measured

by

^Nakaï

et al.

[5]

^{for the}

integral

attenuation coefficients

G2

and

G4 :

The intensities

I.

^and

7g

^{can then be}

written,

^{at 0° :}

These

expressions

^{lead to a value of F as a function}

of the distance d. A

least-square

fit program

gives

^the

best value of the mean

life r,

^{from the} corrected values

F(d)

^{as a function of the distance.}

Figure

^{4 shows}

the

experimental

^data

points

^for

F(d)

^{versus the}

stop- ping ^distance,

^{for the two studied}

energies :

^the

straight

line is the best fit curve.

FIG. 4. ^- Plot of Log

[ (I. iu + is)-l

^{versus the} separation ^dis- L(iu ^u -E- 7s)

tance between target ^and plunger. ^{The lower curve} displays experimental ^{results at 4} MeV, ^{and the} upper ^one the results at 2.9 MeV. The distance origin ^is arbitrary, because it is an

adjustable parameter.

|

.

2022 experimental points.

- best fit curve.

3. EVALUATION OF THE ERROR IN THE MEAN LIFE i. ^- The mean life is

dependant

^on three expe- rimental

parameters fi

⁼

v/c,

^{F and d.}

The error

on f3

^is

easily

calculated from the esti- mate of the center of

gravity

^{of the two} rays. For the

two other sources of _error, we simulated a series of

experiments by replacing

^{in the}

expression

^{of F}

against d,

^the

experimental

^{results F and d}

by pseudo-

random

weighted

values. The series of best fits so

obtained enable us to extract errors

coming

^{from the}

experimental

values of F and d.

844

Results. ^- After corrections as mentioned above and error calculations

including AT(d, F, B),

^we

finally

obtained :

which

gives

the average :

IV. Discussion. ^- After correction due to the internal conversion coefficient as calculated

by

Rose

[6],

^{the mean lifetime}

gives

^{the reduced transition}

probability :

FIG. 5. ^- Comparison ^{between our} results and previous

results. In the lower figure, ^{we show} B(E 2) values, ^{in e2 b2} units, for the 0+ -> 2+ transition. In the _upper figure ^are the intrinsic

quadrupole

^{values in barn.} References are as follow : a) ^Reference [1].

b) ^Reference [7].

c) ^Reference [13].

d) ^Our measurement.

e) ^We calculated Qo ^{with the} expressions (3) ^and (4) using Morand’s [12] ^results.

f ) ^Same calculations using Raynal’s [11] results.

g) ^Reference [8].

h) ^Our result, using the rotational model and the adopted sign

of Qo.

Figure

^{5 shows the}

comparison

between the value of

B(E 2)

^found

by

^our measurement with the results found

by

^{Jones et al.}

[1] ]

and Eswaran et al.

[7].

By using

the rotational

model, the

transition _pro-

bability

^is

directly

^{connected with the intrinsic}

quadru- pole Qo

of the rotational band :

the static

quadrupole

^moment of the studied level

being :

The static

quadrupole

^moment

Q(2+)

^{was measured}

by

^{Nakaï et al.}

[5], [8]

and Schwalm et al.

[9] using

the reorientation effect

[10].

^{We have}

compared

^these

results with the value deduced from eq.

(1)

^and

(2).

On

figure 5,

^{we show the}

comparison

between the result of Nakaï et al.

[8]

^{and our result.}

The intrinsic

quadrupole

^{moment can} also be deduc- ed from the deformation parameters

32

^and

{34.

Using

^{an axial}

symetry

deformation as :

the

ground

^state

quadrupole

^{moment can be written}

as it follows :

with :

We used the

parameters P2

^and

B4

^obtained

by Raynal et

^al.

[11] and by

^Morand

[12]

^{to calculate}

Qo.

On

figure 5,

^{are shown our} results for radii _ro ⁼ 1.2 and 1.4 fm.

Nakaï’s result is near the value

corresponding

^to

ro ⁼ 1.4

fm,

^{and our result seems close to the value}

corresponding

^to ro = 1.2 fm.

In

conclusion,

^our

experimental

^{results seems to}

be a

tangible

^{link in}

testing

^a model between direct measurement on

quadrupole

^{moments and on mean}

lifetimes. In

spite

^{of their small}

difference,

^the results in both methods with

regard

^{to their}

precision

agree well

enough

^{in the} framework of the rotational model.

References

[1] ^JONES

(K.

W.), SCHWARZSCHILD

(A. Z.),

^WARBURTON

(E.

K.) and FossAN

(D. B.), Phys.

Rev.,

1969, 178,

1773.

[2]

^DIAMOND

(R. M.),

^STEPHENS

(F. S.),

^KELLY

(W. H.)

and WARD

(D.), Phys.

^Rev. Letters, 1969, 22, ^546.

[3]

QUÉBERT

(J. L.), ^NAKAÏ

(K.),

^DIAMOND

(R. M.)

^and

STEPHENS (F.

S.),

^Nucl.

Phys.,

1970, ^A 150, ^68.

[4]

^{BEN ZVI}

(I.),

^GILAD

(P.),

^GOLDBERG

(M.),

^GOL-

DRING

(G.),

SCHWARZSCHILD

(A.),

^SPRINZAK

(A.)

and VAGER

(Z.),

^Nucl.

Phys., 1968,

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121,

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[5] ^NAKAÏ

(K.),

^STEPHENS

(F. S.)

^{and DIAMOND}

(R. M.),

Nucl.

Phys., 1970,

^A

150,

^114.

[6]

^ROSE

(M. E.),

^GOERTZEL

(G. H.),

^SPINRAD

(B. I.),

HARR

(J.),

^STRONG

(P.), Phys.

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[7]

^ESWARAN

(M. A.)

and BROUDE

(C.),

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Phys., 1964, 42,

^1311.

[8]

^NAKAÏ

(K.),

^WINTHER

(A.),

^STEPHENS

(F. S.),

^DIA-

MOND

(R. M.),

^{To be}

published

^and

private

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munication.

[9]

^SCHWALM

(D.),

^PovH

(B.), Phys.

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1969, 29B,

103.

[10]

^{DE BOER}

(J.)

and EICHLER

(J.),

Advances in Nuclear

Physics,

^Plenum Press, ^New

York, 1968,

^1.

[11]

^RAYNAL

(J.)

^{and DE} SWINIARSKI

(R.), Colloque

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^MORAND

(B.), Thèse,

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Bordeaux,

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^SKORKA

(J.),

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(J.),

RETZ-SCHMIDT

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