Measurements of some level-widths in 40Ca between 9.5 and 10.5 MeV

Nuclear Physics A462 (1987) 482-490 Nosh-Holland, Amsterdam

~~UREME~

OF SOME LEVE~WIDTHS 10.5 MeV

GU Mu, GU Xi-liang,

GUO

Zhen-di,

Nuclear Science department,

HU Yu-de,

IN “Ca BE~EEN

QIAN

Jing-hua

and YANG

9.5 AND

Fu-jia

Fudan ~~i~rsit~, Shanghai, China

Received 21 May 1986 (Revised 20 July 1986) Abstract: The total widths of the two excited states at 9603.9, 10 321.0 keV and of the doublet at 9864.6, 9868.8 keV in *Ca have been measured with resonance y-ray absorption. The gamma radiations from the 39K(p, y) reaction at E, = 1307.2, 2042.8 and 1595.0 keV have been selected to excite the corresponding levels in %a. The obtained widths of the 9603.9 and 10 321.0 keV levels are 188 *47 and 91 f 15 eV, respectively. The resonance y-ray absorption technique with cross excitation was used in the measurement for the 9864.6,9868.8 keV close-lying doublet. The analysis of experimental results was extended to this special case and the obtained level widths are 100 *24 and 899 f 214eV. In addition, the (p, y) resonant strengths of the 9603.9 and 10 321.0 keV states have also been discussed.

E

NUCLEAR REACTION 40Ca(y, y) E = 9.604, 10.321, 9.865, 9.869 MeV, 39K(p, y). E = 1.3072, 2.0428, 1.595 MeV, measured u(E,). 4”Ca levels deduced r,,, r, resonant strengths. Natural calcium.

1. Introduction There have been many reports on expe~mental studies between 9.5 and 10.5 MeV excitation states in ‘$%a. A good number of data for the excited states in this energy region have been provided. The 9603.9 and 10 321.0 keV states have been studied in the experiments such as 40Ca(p, p’) [ref. ‘)I, 41Ca(T, r~) [ref. *)] and 38Ar(3He, n) [ref. ‘)I. Because of the limitations on energy resolution of these methods, their widths have not been obtained exactly. Eckert4) measured the width of the 10 321.0 keV state with resonance y-ray absorption, but the result of the (p, y) resonant strength S,, deduced from the width of the 10 321.0 keV level measured by Eckert “) was quite different from the later works 5*6).The data have not been recommended in the 1978 compilation by Endt and Van der Leun ‘). In this work, we try to measure the mentioned widths by the method of resonance y-ray absorption. The 9864.6 and 9868.8 keV levels are known as a doublet. Rangan 8, has measured the level width of the 9864.6 keV state with resonance y-ray absorption and the 9868.8 keV state with the (p, y) yield method. In the present experiment, we take the resonance y-ray absorption with cross excitation to measure both the widths at 9864.6 and 9868.8 keV. This method was reported by Van Rinsvelt 9, who had studied 0375-9474/87/$03.50 @ Elsevier Science Publishers (North-Holland Physics Publishing Division)

B.V.

M. Gu et al. /

4oCa

483

the level widths of a doublet and made an approximate experimental analysis. An accurate analysis formula has been extended in this work and the level widths could be extracted directly. The (p, y) resonant strengths S,, of the levels mentioned above adopted in ref. ‘) were obtained with the relative yield measurements by Engelbertink ‘). In the present experiment, they have been determined directly from resonance y-ray absorption. 2. Experimental procedure 2.1. GENERAL

Proton-capture radiation was taken as the gamma source in the resonance y-ray absorption technique for exciting the nuclei in the absorber. The Doppler shift of emitted y-rays was used to compensate the energy loss of nuclear recoil during the process of gamma emission and absorption for obtaining resonant absorption. The transmission rate T(8) of the radiation through the absorber was measured as a function of the angle 8 to the proton beam. From T(0) the level width r, of the absorbing nucleus can be obtained lo). If the emitting nucleus is the same as the absorbing nucleus and the measured levels are a doublet, the maximum (p, y) yields for both levels can be reached simultaneously under the condition of suitable target thickness and proton energy. The two groups of y-rays will be selectively absorbed at different angles by the same two levels, thus four absorption dips should be observed. In our case, since the neighbouring two in the centre were almost overlapping and could not be distinguished, only three dips were observed. One of them was obtained with resonant absorption by the state Ex2 of y-rays deexcited from the state E,, , which was represented by TR,+w (19). Another was the reverse of that and represented by TR2_R1(0). The third corresponded to the resonant absorption of the two groups of y-rays by their own states and was described with TRI,JO). The proton beam provided by the 3 MV Van de Graaff accelerator of Fudan University was retained 3 kA. The target of KI was evaporated onto a 0.3 mm thick tantalum disc, the vacuum of the target chamber was about lop6 Torr and a forced flow of water cooled the target during the resonant absorption measurement. The detectors used were 10 x 10 cm NaI(Tl) and 120 cm3 HpGe. One was used as a main detector for measuring the y-rays through the absorber and the other was used as a monitor. Their qualities were strictly checked. The main detector was placed on a goniometer which can rotate about the target. There was an absorber-collimator system in front of it. 2.2. THE 9603.9 AND

10 321.0 keV STATES

The 9603.9 and 10 321.0 keV levels were excited by the y-rays from the 39K(p, y) reaction at Ep = 1307.2 and 2042.8 keV. From the reaction kinematics it follows that

M. Gu et al. / *Ca

484

the centres of the absorption dips fall at 78.8” and 80.4”, respectively. The target thicknesses of 50 and 100 keV were selected. The experimental set-up has been shown schematically in our earlier publication lo). The collimator consisted of two 1.5cm long lead blocks with 4 mm interval, the distance from the target spot to the rear end of the slit was 25.3 cm. Here the NaI(Tl) detector was used as the major one and the HpGe detector served as a monitor which was located at 55”, 19 cm from the target. The absorption length of metal calcium was 11.6 cm. The dips were measured as a function of the detection angle in steps of 0.5” and 0.25”. The data were taken by moving the detector to and fro over the range of angles until the accumulated counts reached the desired number at each point. The transmission curves observed are shown in figs. 1 and 2. I

,

1

I

1

I

’

I

’

160015001400fj 1300a w 12001100lOOO-

Fig. 1. The absorption of the 9.604 MeV y-rays from the reaction 39K(p, y) at E, = 1307 keV in a 11.6 cm thick Ca absorber, as a function of the detection angle. The solid line represents the best fit to the data with a gaussian instrumental function.

2.3 THE 9864.6 AND 9868.8 keV STATES

Since the 9864.6 and 9868.8 keV levels are a close-lying doublet, two groups of the y-rays would be emitted from the 39K(p, y) reaction at I?,,= 1595 keV with 100 keV target thickness. They would be selectively absorbed at different angles by the same two levels. Thus three abso~tion dips should be observed. From the reaction kinematics, the expected centres of the absorption dips should fall at 61.8”, 79.6” and 96.3”, respectively.

M. Gu et al. / @Ca -I

,

1

1

1

,

1

I

1

485 ,

1

-

,

llO(

v) z : 0

loot

90(

J

1

80

70

1

1

82

a4

B(ded

Fig. 2. The absorption of the 10.321 MeV y-rays from the reaction 39K(p, y) at E, = 2043 keV in a 11.6 cm thick Ca absorber, as a function of the detection angle. The solid line represents the best fit to the data with a gaussian instrumental function.

’

I

’

I

I

I

1

1

’

I

’

I

1

I

1300

1200 Ln F z 0 1100

1000

900

77

I

79

I

81

1 83

6kJed Fig. 3. The widths of the 9.865 and 9.869 MeV doublet in 40Ca measured For interpretation, see text.

with resonance

y-ray absorption.

M. Gu et al. / 4oCa

486

The experimental set-up was almost the same as formerly described. The distance from the target spot to the rear end of the slit was changed to 23.6 cm. The HpGe detector was used as the major detector and the NaI(Tl) 25 cm from the target as the monitor. The centre dip which corresponded to the absorption of the two groups of y-rays by their own states has been observed, as shown in fig. 3. The goniometer with absorber, collimator and detector was rotated about the target at O.S”/step in the measurement. The procedure was repeated back and forth until the accumulated counts reached the desired number at each point. The spectrum obtained by the HpGe detector is shown in fig. 4. The other two satellite dips have not been shown here. The background, including the counts from natural and off-resonance, was subtracted from the experimental data. 3. Results and analysis The general form of the transmission rate T(8) is a doubfe convolution:

T(B) =

I

dE

I

I dE

d@‘g(E, e’)~(e’-e)~(~) (1)

t

.I

de’ g(E, e’)h(e’-

e)

where h( 8’- 0) represents the instrumental resolution function discussed thoroughly by Biesiot I’), g( E, e’) is the emitter function with the Breit-Wigner shape, whereas T(E) is the transmission function which can be written as T(E)=exp

(2)

,

where F, is the total width of absorber level, n is the number of absorber nuclei per unit area perpendicular to the y-radiation, u. is the maximum resonant cross section, E and E, represent the -y-ray energy and the resonant energy lo), respectively. To the doublet in this experiment the transmission rate T( 8) should be extended. If gi(E, e’), gz(E, S’), hr(@‘- e), h2(8’- 8) and T,(E), T,(E) represent the emitter functions, the instrumental resolution functions and the transmission functions of the states Exl and Ex2, respectively, the reformed transmission rates for the three dips are as follows:

TRI+R2(e) =

I

dE

I

de’[g,(E,

e’)~~(e’-e~T~(E)+g*(E,

eyh,(e’-e)] ,

df?‘[g,(E, fY)h,(e’--6)+gz(E,

e’)h,(f--e)]

(34

M. Gu et al. 1 4oCa

487

81-

(SE)

61 -

9.86 MeV (FP)

0 4100

6000

5525

5050

4575

CHANNEL

Fig. 4. Part ofthe

y-ray spectrum

JJ dE

k,r&9

of the HpGe detector deexcited states.

=

de’[gr(E,

I

from the 9.865 and 9.869 MeV resonance

e’)h,(e’-e)T,(E)+g*(E,

O’)h,(e-@T,(E)] 9

dE

I

de’[g,(E,

eyt,(e’-e)+g,(E,

ef)h2(ef-e)] (3b)

T RZ-+RI(e) =

I

dE

I

I dE

de’ [g,(E, e’)hl(e’-

J

de’[gl(E,

e) +g,(E,

e’)h,(e’-

e)+g@,

eyh2(e’-

e)z-,(E)]

e’)hz(e’-

e)]

9

(3c)

where 8 is the angle between the proton beam and the centre of the collimator slit, E is the y-ray energy, and 8’ is the angle between the proton beam and emitter y-ray. The expressions of instrumental resolution function and the transmission function are the same as those mentioned above except the emitter function. While two groups of y-rays exist, the emitter function must show the relative strengths of them, 1

g(E~e’)=(2~+1)(210+1) x [i + U,P,(COS

1 [(E-Ee(6”))2+(;~e)2]

et) +

u,P.+(cos

ey] ,

G resp,, r,, (4)

488

M. Gu et al. / 4oCa TABLET The widths of the 9603.9 keV and 10 321.0 keV states and the 9864.6 and 9868.8 keV doublet in %a obtained with resonance y-ray absorption

r

E, &eV) 9603.9 10 321.0

r,, (ev)

(ev)

4.9+ 1.8 6.6 f 0.8 3.6 f 0.24 “)

188*47 91*15 10.3* 1.7 “) 100*24 110*30b)

9864.6 9868.9

899*214 1060 * 200 b,

X2

nfl0

0.54*0.14 1.30*0.15

0.6 1.3

0.63kO.11

0.4

0.03:; A:

0.4

“) The data from ref. “). b, The values adopted from ref. *).

where s and I, are the spins of the incident proton and target nucleus, r,,,/r, is the fraction of y-decay to the ground state, S,,, is the (p, y) resonant strength, r, is the level width of the emitting nucleus, P,(cos 0’) and P,(cos e’) are Legendre polynomials, a, and a4 are parameters of the gamma angular distribution from the (p, y) reaction, E,(e’) is the emitter energy lo) of -y-rays from compound nuclei at an angle 0’. Since the instrumental resolution function is determined by both the collimator slit and the angular divergence of the proton, the instrumental resolution functions can be approximately regarded as the same to a doublet. Thus eq. (3) can be simplified as

T(B) =

I

dE

I

de’[gr(E, e’)+gz(E,

e’)lh(e’-e>[T,(E)+T,(E)I

dE , de’[g,(E,

e’)]h(ef-e)

J r

-1. 8’)+gz(E,

(5)

The experimental results shown in figs. 1, 2 and 3 were analyzed with computer code which performed a standard x2 search for the optimal parameter set. The computations were based upon the transmission rate formulae, eqs. (1) and (5). In the calculations we have used the results obtained by Rangan “) and Leenhouts 6, for the angular distributions and the fractions of the y-decays to the ground state. In table 1 the results are given for r, r,, and na, of the absorber states. For comparison, we have also shown the results of other authors. 4. Discussions The level widths in “‘?a have been measured with resonance y-ray absorption. From these results, the (p, y) resonant strengths for 9603.9 keV and 10 321.0 keV could be deduced.

M. Gu et al. / 4oCa

From the fitting procedure have been obtained

of experimental

489

data the nao parameters

in sect. 3. The nu, can further

be expressed

of the levels

as

where n is the number of absorber nuclei per unit area perpendicular to the y-radiation, r,, and r, are the width of the y-decay to the ground state and the total width of the absorber level, respectively. The statistical factor g= (25, + 1)/(25, + l), where J,, and Jg are the spins of the excited state and the ground state of the absorber, and A is the wavelength of the radiation. If r, = rp+ r,, then

(7)

when r, obvious measured Since in 40Ca,

3 r,, the negative root is selected; otherwise, the positive is chosen. It is can be absolutely that the (p, 7) resonant strength S,, (25, + l)TJ,/T, with resonance y-ray absorption. the (p, y) resonant strength of the 10 321.0 keV state is the strongest one its value is often used as a standard to calibrate that of the other levels in

4oCa in the relative measurement. Eckert 4), Leenhouts “) and Engelbertink ‘) have given the S,, value of this level. Nowadays the accepted datum published in ref. ‘) came from Engelbertink in his relative measurements, where the resonant strength S,, of 3oSi(p, Y)~IP reaction at E, = 622 keV was used as the absolute standard which was obtained by using the resonance y-ray absorption 12). The S,, from Engelbertink is equal to 31*5 eV. It may be better obtained directly with the resonance y-ray absorption than with the relative measurement. Since the S,, analysis is related to the emitting channels according to eq. (7), it is necessary to prove whether the other channels are open besides proton and gamma ones. Depending upon the threshold energy of the nuclear reaction, the 10 321.0 keV state should have not only proton and gamma channels but also an alpha one. A solid track detector

that is sensitive

to cz-particles

was used in our experiment,

but there was

no alpha to be seen. This is consistent with the explanation of charge independence of nuclear force. Using eqs. (6) and (7) to deal with the resonant absorption, the S,,, value of the 10 321.0 keV state was directly deduced as 20.3 f 3.3 eV. The fraction of the -y-decay to the ground state used in our calculation of 90% [ref. “)I might bring some error to our results. Since the 9603.9 keV level in 40Ca decays completely to the ground state 13) and also has the powerful (p, y) resonant strength, it is more suitable to obtain its S,, directly from the resonance y-ray absorption to serve as the absolute standard in relative measurement. With the same method, the resonant strength of the 9603.9 keV state was deduced as 14.lk3.5 eV. The S,, given by Engelbertink ‘) in 1966 was 11 eV and no error was given.

490

M. Gueial./40Ca

References 1) C.R. Gruhn, T.Y.T. Kuo, C.J. Maggiore, H. McManus, F. Petrovich and B.M. Preedom, Phys. Rev. C6 (1972) 915 2) D. Cline, M.J.A. de Voigt, P.B. Void, 0. Hansen, 0. Nathan and D. Sinclair, Nucl. Phys. A233 (1974) 91 3) W. Bohne, K.D. Buchs, H. Fuchs, K. Grab&h, D. Hilscher, U. Janetzki, U. Jahnke, H. Kluge, T.G. Masterson and H. Morgenstern, Nucl. Phys. A284 (1977) 14 4) A.C. Eckert and E.F. Shrader, Phys. Rev. 124 (1961) 1541 5) G.A.P. Engelbertink and P.M. Endt, Nucl. Phys. 88 (1966) 12 6) H.P. Leenhouts and P.M. Endt, Physica 32 (1966) 322 7) P.M. Endt and C. van der Leun, Nucl. Phys. A310 (1978) 1 8) L.K. Rangan, G.I. Harris and L.W. Seagondollar, Phys. Rev. 127 (1962) 2180 9) H. Van Rinsvelt, Physica 30 (1964) 59 10) Guo Zhen-di, Gu Xi-liang, Hu Yu-de, Qian Jing-hua, Chen Zheng-guo, Gu Mu and Yang Fu-jia, Scientia Sinica A29 (1986) 92 11) W. Biesoit and P.B. Smith, Phys. Rev. C24 (1981) 2443 12) P.B. Smith and P.M. Endt, Phys. Rev. 110 (1958) 1442 13) R.J. de Meijer, A.A. Sieders, H.A.A. Landman and G. de Roos, Nucl. Phys. A155 (1970) 109