Gamma rays from the 4.24 MeV state in magnesium-24

l.D.2: l.E.4;

Nuclear PJi,ysics 16 (1960) 38-51;

© North-Holland Publishing Co., Amsterdam

Not to be reproduced by photoprint or microfilm without written permission from the publisher

3.A

GAMMA RAYS FROM THE 4.24 MeV STATE IN MAGNESIUM-24 J. FERGUSON, H. E. GaVE and A. E. LITHERLAND Chalk River Laboratories, Chalk River, Ontario, Canada

R. BATCHELOR t, A.

Received 4 December 1959

Abstract: The Mg24(p, p'y)Mg24 reaction has been studied in the proton energy range from 5 MeV to 6 MeV. The yield of 4.24 MeV y-rays shows two resonances, at 5.24 MeV and 5.72 MeV, corresponding to states in Alu at 7.30 MeV and 7.77 MeV. The total widths of these resonances are 100±20 keV and 340±50 keV. Angular distributions and correlations of the ,..-rays from the 4.24 MeV state of Mg24 measured at the 5.72 MeV resonance show that the 4.24 MeV state has spin 2. Spins of 1 and 3 are eliminated by the measurements. The spin of the 7.77 MeV state of Al"5 is most probably t. The measured branching ratio of the y-rays from the 4.24 MeV state to the ground and 1.37 MeV states is (2.9±O.5) : 1 and the E2{MI amplitude ratio for the 2.87 MeV transition is +23± 9. These data give qualitative support to the collective model but there are quantitative disagreements with the detailed predictions for both axially symmetric and asymmetric nuclei.

1. Introduction The nucleus Mg 2!l is of considerable interest since the available information on its low-lying level structure 1,2) suggests that it has a spheroidal shape. The level scheme is shown in fig. 1. Extensive use has been made of the ,a-decay of Na 24 to Mg 24 to study the first two excited states and the properties of these are now well established 3). There are, however, very few measurements pertaining to the 4.24 MeV and higher levels. Newton 4) observed the capture y-radiation from the bombardment of Na 23 by protons and showed that the 4.24 MeV level decayed both to the ground state and the 1.37 MeV level. From angular distribution and correlation measurements its spin was deduced to be 2. An even parity was assigned from the fact that the ,a-transition to the state was second or higher forbidden 5), and this is confirmed by observed l = 2, 1 = 0, transitions to the unresolved levels at 4.12 and 4.24 MeV in the Na 23(d, n)Mg 24 reaction 6,7). Newton's letter, however, gave very few experimental details. As can be seen, the level scheme is in good qualitative accord 'with the collective model B). The first three levels can be interpreted as constituting the first three members of a K = 0 rotational band and the 4.24 MeV level could be the first member of aK = 2 band. The spin 3 level at 5.24 MeV could be the second t Seconded from the United Kingdom Atomic Energy Authcrity, Atomic Weapons Research Establishment, Aldermaston. 38

GAMMA RAYS FROM THE 4.24 MeV STATE IN MAGNESIUM-24

39

member of the K. = 2 band, if its parity is even, but at present its parity is assigned a doubtful negative 9). The branching ratio of the de-excitation y-rays of the 4.24 MeV level to the ground state and 1.37 MeVlevel, as measured by Newton, agrees exactly with the predicted value of 5, assuming that the 2.87 MeV radiation is pure quadrupole. The level scheme can also be considered in terms of collective excitations with violation of axial symmetry. Davydov and Filippov 10) show that, in the case of an even nucleus, the rotational spectrum is only slightly affected by the axial asymmetry, but new rotational states with angular momentum 2, 3,·4 etc. appear. Van Patter 11) has recently surveyed the experimental data regarding E2 transitions from the second 2+ levels in even nuclei, showing that the predictions of this model are quite well borne out. For Mg 24 , however, the preJ7T

MeV

5.24 - - - - - 3(-) 4.24 12 2

4.

11

2+ 4

+

,.,"~" JLo. Fig. 1. Level scheme of Mg". (The branching ratio of the 4.24 MeV level is the result of the present experiment. )

dieted value of the branching ratio from the 4.24 MeV level is 0.88 which is definitely not in agreement with that measured by Newton. In the present experiment the y-rays from the 4.24 MeV level have been studied through the inelastic scattering of protons by Mg 24 . At the bombarding energies used, between 5 and 6 MeV, inelastic scattering to the 1.37 MeV and 4.24 MeV levels are the predominant reaction channels. Angular distributions of the 4.24 MeV and the 2.87 MeV y-rays with respect to the proton beam and also the correlations of the 2.87 MeV and 1.37MeV y-rays, all with the intermediate proton radiation unobserved, have been measured. The results have been analyzed, by a method first suggested by Warburton and Rose 12) and later developed by Litherland and Ferguson IS), to check the spin assignment 2 for the 4.24 MeV state. In this analysis, which is described in detail in ref. IS), the correlations are expressed as an incoherent sum over the correlations from the different substates of the first gamma-ray emitting state of the residual nucleus. Consequently the considerations of the details of

40

R. BA:rCHELOR, A.

J.

FERGUSON, H. E. GOVE AND A. E. LI:rHERLAND

the formation and decay of the compound nucleus are simplified. The present experiment, in which the analysis is simplified further by the target nucleus having zero spin, is the first of a series on various light nuclei to which this analysis will be applied.

2. Experimental Procedure The measurements reported here were made with the Chalk River Tandem Accelerator. The proton beam was focussed down to about inch diameter at the target by magnetic quadrupole lenses situated approximately equidistant from the analyzer magnet and the target. The proton energy was known from a previous calibration of the analyzer magnet using known (p, n) thresholds 14). The gamma rays were observed by two NaI(Tl) scintillators, one 5-inch diameter by 6-inch long and the other 5-inch diameter by 4-inch long, each placed with its front face 6.5-inch from the centre of the target. Each crystal had a }inch thick lead absorber placed in front to cut down the counting rate from the coulomb excitation of the gold backing. For angular distribution measurements the former was rotated and the latter acted as a monitor fixed at 900 to the direction of the incident proton beam. For the angular correlation measurements, the 5-inch by 4-inch crystal was again fixed at 90 0 • In the so-called geometry A a channel was placed on the total absorption peak of the 1.37 MeV gamma-ray in the pulse-height spectrum from the 5-inch by 4-inch crystal and in geometry B the channel was placed on the total absorption peak of the 2.87 MeV gamma ray. These geometrical arrangements of the counters are shown in fig. 5. After amplification, each pulse-height spectrum was displayed on a IOO-channel transistorized pulse-height analyzer. A conventional fast-slow coincidence circuit 15), with a resolving time 21' of about 50 ns was used for the correlation measurements. Most of the measurements were made with a natural magnesium target, of thickness approximately 2.5 mg/cm 2, on a gold backing; a few, however, were made with separated Mg24, of thickness about 100flg/cm2, on a tantalum backing and supplied by the Electromagnetic Separator Group, Atomic Energy Research Establishment, Harwell, England. Preliminary experiments were first made to establish that the radiations observed came mainly from the de-excitation of the 4.24 MeV level and not the 4.12 MeV and 5.24 MeV levels. Fig. 2 shows the pulse-height distributions obtained at 5.72 MeV proton bombarding energy from the 5-inch by 6-inch crystal for the natural magnesium (curve a) and separated Mg24 (curve b) targets. These measurements were made with the detector at 900 to the incident beam direction. The energy scale was established with various radioactive sources including a Na24 source, the pulse-height distribution from which is also shown in fig. 2 (curve c). Negative ,a-emission from Na 24 predominantly

i

GAMMA RAYS FROM THE 4.24 MeV STATE IN MAGNESIUM-24

41

feeds the 4.12 MeV level of Mg 24 which then decays through the 1.37 MeV level. Comparison of the relative positions of the 2.75 MeV peak in curve (c) and the peak labelled (2) in curve (a) shows quite conclusively that the latter is at 2.87 MeV, and hence is from the decay of the 4.24 MeV level. Moreover, the peaks (I) and (2) are not wider than those from single energy groups. (The full width at half height of the 2.61 MeVtotal absorption peak from a The" source for the 5-inch by 6-inch crystal has been measured to be 5.5 %). This implies E: y (MeV) 10'

1.0

2.0

3.0

4.0

5.0

(4)

...J 10'

ur

z z

«

:r: u

IJJ

.... Z

:J

~ JO~

I 0 o'::---'---::L 2 0=-'--4'"="0--'--='6O::-'-""""'S='"=O....:.L.--:-:'I00

CHANNEL NUMBER

Fig. 2. Pulse height distributions from 5-inch by 6-inch crystal at E p = 5.72 MeV and at 90° to the beam direction for natural magnesium target (curve a) and separated Mg" target (curve b). Curve c is the distribution obtained with a Na 24 source.

that inelastic scattering at this bombarding energy does not noticeably excite the 4.12 MeV level. There is also no suggestion of a peak at 3.87 MeV which would arise from the decay of the 5.24 MeV level through the 1.37 MeV level. The peak labelled (3) at 1.83 MeV in curve (a) does not appearincurve (b), and is most likely due to radiation from the first excited state of Mg26. The broadening of the 4.14 MeV peak in curve (b) is due to 4.43 MeVradiation from inelastic scattering by carbon, which contaminates the target. This effect is not noticeable in curve (a) because the target used is much thicker, and hence has a greater ratio of magnesium to carbon. The yield of 4.24 MeV y-rays was measured as a function of proton energy,

42

R. BATCHELOR, A.

J. FERGUSON, H. E. GOVE AND A. E. LITHERLAND

using the separated target. As seen in fig. 3, two resonances at 5.24 MeV and 5.72 MeV are seen. Strong resonances at these energies were not observed by Seward.") in the yield of the Mg 24 (p, p')Mg24* reaction, leaving Mg 24 in the 1.37 MeV state, although there was perhaps a slight resonance at about 5.2 MeV. EXCITATION IN

Alz ,

(MeV)

7.0 7.2 7.4 7.6 7.8 8.0

4

o4.6'::--='::--:i>::"-;.:'-;;-;:'-:--cf:::-!-:::-!-:::--:f::--::' 4.6 5.0 5.2 5.4 5.6 5.8 6.0 6.2 6,4 E p (MeV)'LAB

Fig. 3. The 90° yield of 4.24 MeVy-rays obtained with separated Mg24 target, thickness

i">J

5 keV.

Angular distributions were taken on both resonances using the natural magnesium target; angular correlations of the gamma rays measured in coincidence in geometry A and B were taken at 5.72 MeV only.

3. Results Fig. 4 shows a linear plot of the pulse-height distribution from the 5-inch by 6-inch crystal, at 900 to the incident beam direction, and at 5.72 MeV bombarding energy using the natural magnesium target. A similar curve was obtained ...J

2.87 MeV

t

W

z

:i 2000 :I: U

n:: W

a. Ul 1000

IZ :::J

... ---

o

U

o

10

20

30

40

50

60

70

100

CHANNEL NUMBER

Fig. 4. Pulse height distribution from 5-inch by 6-inch crystal at E p = 5.72 MeV, () = 90°. The dotted curve is the fitted line shape of the 4.24 MeV ?,-ray.

43

GAMMA RAYS FROM THE 4.24 MeV STATE IN MAGNESIUM-24

with the 5-inch by 4-inch crystal. Typical coincidence spectra obtained in geometries A and B are shown in figs. 5(a) and (b). In geometry A, peaks in addition to, and at energies lower than, the 2.87 MeV peak are observed since the window around the 1.37 MeV peak in the 5-inch by 6-inch crystal includes the tails of spectra from y-rays greater than 1.37 MeV. The peaks at 1.14 MeV and 1.83 MeV are due to cascade radiations from the second level in Mg 26 at 2.97 MeV. In agreement with the deductions made from fig. 2 concerning the possible excitation of the 4.12 MeV level this curve shows no positive indication of a 2.76 MeVy-ray. By comparing the peak to valley ratio ofthe 2.87 MeV peak in fig. 5(a) with that for a 2.61 MeV peak (obtained with a The" source) we estimate an upper limit of 0.1 for the ratio of the intensities of the 2.75 MeV and 2.87 MeV y-rays. For geometry B there is a small but significant counting rate Ey (MeV) 2 :3

EylMeV) 2

...J W Z Z

«

:J:

1.14 MeV 200

u

0::: w o,

150

~ z

::J

o

r1.37 MeV

r{37MeV

!

(b)

(0)

r1.83 MeV r2.87 MeV

U

w u

z

w o

50

U

z

8

20

20 40 60 80 CHANNEL NUMBER

Fig. 5. Coincidence spectra at E p

40

60

80

CHANNEL NUMBER

=

5.72 MeV. (a) Geometry A. (b) Geometry B.

above background just below 2 MeV which is probably due to cascade radiation from high energy states in magnesium-26. The angular distributions and correlations of the cascade y-rays from the 4.24 MeV level were computed from the number of counts in the appropriate total absorption peaks in the observed spectra. In general this was relatively straightforward. For example the number of counts in the 4.24 MeV peak in the curve of fig. 4 was obtained by extrapolating the background observed beyond the peak, summing the total and background counts between the vertical lines A and B, and taking the difference. Estimation of the counts in the 2.87 MeV peak is however, much less certain, since the background to be subtracted is relatively large and cannot be measured directly. This background is made up of two contributions, that from the tail of the 4.24 MeV peak, and that from

44

R. BATCHELOR, A. J. FERGUSON, H. E. GOVE AND

A. E. LITHERLAND

other radiations, such as neutrons from (p, n) reactions with the target nuclei (Mg25, Mg26 and gold), and low intensity y-rays which are not sufficiently strong to show definite peaks (for example a 3.87 MeV y-ray from the decay of the 5.24 MeV level). A lower limit to the background was estimated from a measurement of the spectral line shape of a 4.43 MeV y-ray. which is very close in energy to 4.24 MeV, and normalizing this to fit the 4.24 MeV total absorption peak. The measurement was made by bombarding a CU(NOS)2 target, with the nitrogen enriched in N15, with 3 MeV protons and observing the 4.43 MeV y-rays emitted in the reaction N15(p, cx.y)02. No other prominent y-rays are produced in the reactions of protons with N15 at this bombarding energy. The fitted line shape is shown as the dotted curve in fig. 4. An upper limit to the background was taken to be the sum of the counts under the full curve in fig. 4 between the vertical lines C and D, the distance between which is equal to the distance between the lines D and E encompassing the 2.87 MeV peak. The angular distributions of the 2.87 MeV y-rays were computed using both these background assumptions. The polynomial coefficients obtained agreed within the statistical errors and hence mean values were taken to obtain the final answers. All the experimental data pertaining to the various angular distributions and correlations, not corrected for the finite angle subtended by the detector, are presented in figs. 6 and 7 and tables 1 and 2. The experimental correlation coefficients shown in the tables were obtained by least squares fitting of the data, for even terms up to P4' by the Chalk River Datatron computer. The errors given in tables 1 and 2 do not include (a) the effects of the small, but finite, contributions from the other magnesium isotopes and (b) the effect of the small < 10 % contribution from the cascading gamma rays from the 4.14 MeV excited state in Mg 24. Upper and lower limits for the branching ratio 1uJ12 •87 of the 4.24 MeV level have been calculated using the two background assumptions for the 2.87 MeV peak discussed above. The calculation proceeded with an area analysis of the 90° spectra recorded by the 5-inch by 4-inch crystal, the efficiency of which has been previously measured by Gove 17), and then integration over 4n using the measured angular distribution coefficients. The correction for the difference in the attenuation of the two {'-rays by the lead shield was negligible. The values obtained are 1 at E p = 5.72 MeV, 2 .6 < 1 4.24 < 3. 6-, 2.87

1

~ < 3.1. 1 2•87 The average value of the ratio is taken to be 2.9±0.5.

at E p

5 24 =.

Me, V

2.3

<

45

GAMMA RAYS FROM THE 4.24 MeV STATE IN MAGNESIUM-24

4. Theoretical Analysis of the Angular Distributions and Correlations Although a detailed theoretical treatment of the angular correlation analysis is to be found in ref. 13), the general outline of the procedure will be discussed here. Let Jl' J2 andl denote the spins of the 4.24 MeV, 1.37 MeV and ground states of Mg24 , and let 2 L1, 2L2 and 2 L12 be the multipolarities of the 4.24 MeV, 1.37 MeV and 2.87 MeV y-rays. Since the inelastic protons are not observed, the state Jl is formed in an axially symmetric way. The angular distribution of the 4.24 MeV is then given by W(81) = (-ll-m+L 1+L'l H kQk P (m) m k • Udlm-mlkO)Zl(Ll11L'lJl' lk)Pk(cos ( 1 ), (1) where

:Lz

Qk is an attenuation factor representing the correction to the Legendre polynomial coefficient for the finite angle subtended by the detector 18), P(m) is the relative population of the substate m of the state Jl' and is equal to P(-m), Udlm-m\kO) is a Clebsch-Gordan coefficient, ZI(L111 L'111, Ik) is a coefficient defined and tabulated by Sharp et al. 19 ) . The angular distribution of the 2.87 MeV y-rays is given by an expression similar to (1) with 81 , land L 1 replaced by 812 , J2 and L 12 , respectively. The general form of an angular correlation of the y-rays from the axially symmetric state Jl is W t t ,(812 , 82 , 4» =

L

KMN

:L(-I)L2+L'2QKQMT(s)D~M(tt')X~M(812' 82 ,

r/».

(2)

8

The quantities T (s) specify the alignment of the state Jl' and are related to the populations P(m) by the equation

P(m)

=:L T(s) (sJlm-mllO)2, s

where the quantum numbers t satisfy the relation 8+1 = J 1 .

The angle 4> is the aximuthal angle of the 2.87 MeV y-ray relative to the plane containing the beam and the 1.37 MeV y-ray. Corrections for the finite angles subtended by the two detectors are introduced through the factors QK and QM' The coefficients D~M(tt') and X~M(e12' 82 , r/» have previously been defined by Ferguson and Rutledge 20). t The angular momentum quantum number 1is chosen so that the D~M(tt') coefficients can be obtained from the tables of Ferguson and Rutledge 30). For the calculations discussed in this paper it was found convenient to choose 1 = ]1'

46

R. BATCHEJ:.OR, A. ]. FERGUSON, H. E. GOVE AND A. E. LITHERLAND

In the correlations measured here one of the counters was fixed at 90° to the beam direction and the other moved in the plane of the beam and first counter. Hence eq. (2) can be simplified to Ww(lJ} =

where

LL T(s)A1'P1'(cos 8), l'

•

(4)

L IY.~MQKQMD!J<:M(tn· KMN The coefficients IY.~KM and D!J<:M(tt') have been tabulated by Ferguson and Rutledge 20). In the present analysis the attenuation factors Q have been taken from calculations by Gove and Rutledge 21) for a 5-inch by s-inch crystal and by Rutledge 22) for a 5-inch by 6-inch crystal. In these calculations it was assumed that all pulses produced by the y-ray interactions in the crystal are included in the analysis of the experimental data. In the present experiments only the pulses in the total absorption peaks are computed and hence the attenuation factors used are over-estimates of the actual values. However, the overall errors introduced are small since the uncertainties in the attenuation factors represent errors in applied corrections. Taking the spins of the 1.37 MeV and ground states of Mg 24 as 2 and 0, respectively; we see that the unknown quantities in eqs. (1) and (4) are 11' the multipole mixture of the 2.87 MeV transition and the quantities T(s). The measured angular distribution and correlation coefficients provide sufficient data to solve for these unknowns. The analysis, in fact, proceeded by assuming a value of II = 2 and then seeking a consistent set of theoretical fits to all the data. The observations provided 12 polynomial coefficients, and seven parameters had to be fitted. These parameters are the ratios T(l}jT(O) and T(2)/T(O), the quadrupole/dipole mixture of the 2.87 MeV transition, and four normalization factors, one for each correlation. The parameters occur non-linearly and the fits were effected with the assistance of the non-linear least squares sub-routine of the Chalk River Datatron. The analysis was performed with and without the attenuation corrections Q applied and the fitted curves are shown in figs. 6 and 7. The fits using the attenuation factors appropriate to this experiment would lie between the solid (with attenuation corrections) and dashed (without attenuation corrections) curves. The theoretical polynomial coefficients (with attenuation corrections) are compared with the experimental coefficients in tables 1 and 2. Forthese fits the ratios T(l}JT(O) and T(2)/T(0) are 1.64±O.06 and 0.30±O.07, respectively, and the quadrupole/dipole amplitude ratio of the 2.87 MeV transition is +23±9. From eq. (3) the ratios P(l)jP(O) and P(2)JP(0) are O.77±0.06 and O.09±O.03, respectively. Figs. 6 and 7 show that the experimental data can be fitted well with 11 = 2. It is now necessary to consider if the data are consistent with other values of 11' A 1' =

47

GAMMA RAYS FROM THE 4.24 MeV STATE IN MAGNESIUM-24

Values of Jl = 1 and 3 only need be considered since Jl = 0 is ruled out by the observation that the state decays to the ground state, and 'With II > 3, the high multipole transition to the ground state is very improbable t. To check the 18

18

£p = 5.72 MeV 16

4.24 MeV (y-RAY

14

Ep = 5.24 MeV

..

16

12

.• •

••

10 8

.

14

4.24 MeV (Y-RAY

••

10 8

2.87 MeV y-RAY ~

12

6~

2.87 MeV )I-RAY ••••

4

•

~Il

•

6

•

•

•

4

o Fig. 6. Angular distributions of the 4.24 MeV and 2.87 MeVy-rays at E p = 5.72 MeV and 5.24 MeV. The solid curves are the theoretical fits for 11 = 2 with corrections for finite solid angle. The dashed curves are the theoretical fits for 11 = 2 without corrections for finite solid angle.

W 14

!;{

~

::

z

~

8

lJJ

6

U

>

~

t;j 0::

f~ Vi f~ t j ~ / ' ~ .I 1.37 MeV

~

-

2.87 MeV

!

J

!

I~

1 /

./1

' ........... /

. . __ ",

7

: 4

~/'

I

-,

r. "

:3

4

2

GEOM ETRY

2

o

20

40

60

e~2

60

A 100

GEOMETRY 0

20

40

60

e;

80

B 100

Fig. 7. Angular correlations at E p = 5.72 MeV. Key for curves is similar to that for fig. 6.

consistency of the data 'With II = 1 or 3, the analysis proceeded by first calculating the parameters P(m) and the multipole mixture of the 2.87 MeV transition required to fit the two measured angular distribution coefficients. These calculated parameters were then substituted in eq. (4), 'With no attenuation corrections applied, to predict the two angular correlations. Since the multipole mixture is two valued, two sets of correlations for each value of Jl are predicted. t Calculations of the gamma-ray correlations from an aligned nucleus for the case = o have been published by Cox and Tolhoek 23).

12 = 2, 1

1 1 = 4,

48

J. FERGUSON, H. E. GaVE AND A. E. LITHERLAND

R. BATCHELOR, A.

TABU; 1

Angular distribution coefficients

Ep (MeV)

I

5.72

Ey 4.24

2.87

5.72

5.24

a.la o

I

(MeV)

Expt. Theory (II

=

+ 0.398± 0.014 2) +0.393

-0.013±0.017 -0.002

Expt. Theory (Jl

=

-0.147±0.015 2) -0.119

+0.010±0.010 0

4.24-

, Expt.

+0.251±0.O09! +0.034±0.018

2.87

I

-0.050±0.030

1 5.24

,

a,lao

I

Expt,

TABLE

I + 0.010± 0.050

2

Angular correlation coefficients at E p = 5.72 MeV

a21 ao

I Geometry A

Geometry B

I

Expt. Theory (II

j Expt. Theory (II

a,lao

I

=

- 0.373± 0. 035 2) -0.442

=

-0.285±0.07 2) -0.4-01

+0.278±0.04-7 +0.292

1

j

+0.160±0.09 +0.318

TABLE 3 Predicted angular correlation coefficients for II

Geom, A B A B A B A B

A (expt) B (expt)

III I

~ I~ \ I

1

I: I I; I I I

E2/M1

1.31 1.31 0.38 0.38 2.33 2.33 -0.01 -0.01

I I I 1

I I

a.lao -0.610 -0.407 -0.530 -0.569 +0.432 +0.764-0.007 +0.338 -0.373 -0.285

I I

I

I I I

=

1 and 3

a,la o -0.389 +0.012 -0.082 +0.54-9 -0.200 -0.239 0 -0.014 +0.278 +0.169

These are shown in table 3 and, for comparison, the experimental values are also included. Although these predicted values have been obtained without applying the attenuation corrections and also do not represent least squares fitting of the data, as in the case of II = 2, they are sufficient to show that the data is not consistent with II = 1 or 3. The best fits in table 3 are for II = 1 but these have the wrong sign of the P4 coefficient for geometry A.

GAMMA RAYS FROM THE 4.24. MeV STATE IN MAGNESIUM-2<1

49

5. Discussion The results of this experiment, combined with the results of previous work (see Introduction) confirm the assignments 2+, 2+and 0+ for the 4.24 MeV, 1.37 MeV and ground states of Mg24. The feasibility of the relatively simple approach to the interpretations of triple correlations, as developed by Litherland and Ferguson, has also been demonstrated. An interesting outcome of the theoretical analysis arises from the similarity of the angular correlations in geometry A and B. It can be shown that if 12 = L 2 = L 12 and if I = 0, then the two coefficients D~M and Dr:.ll( are equal and hence geometry A and B correlations should be identical. This was observed to be approximately the case, implying that the La radiation is predominantly E2. The two resonances found in the yield of the 4.24 MeV y-rays correspond to levels in A12 6 at 7.30±0.03 and 7.77±0.04 MeV, respectively, taking the binding energy of the proton as 2.28 MeV. The thickness of the separated MgM target, approximately 5 keV at the bombarding energies used, is much less than the experimentally observed widths, which are 100±20 keV and 340±50 keV, respectively. The tensor parameters P,cO (see for example Devons and Goldfarb 2<1)) describing the 4.24 MeV state can be obtained from the population of the magnetic substates from the formula PkO

=.L (-I)h-mUdlm-mlkO)P(m).

(5)

m

Using the values of F(m) quoted in section 4, we find that P20/POO = -O.71±O.03 and P40!POO = O.OO±O.03. The following argument suggests that the spin of the 7.77 MeVlevel of A126 is most probably t. The tensor parameters P'eO can be derived on the assumption that the reaction proceeds through the formation of a well defined state of the compound nucleus. It can readily be shown 24) that the expression for PkO then contains Racah coefficients W(ljlj, tk), where land i are the angular momenta of the incoming proton wave and the compound state. Since only the values of Poo and P20 are significant and k is even and :::::; 2j, it follows that i most probably has a value l Qualitatively the data obtained in this experiment are in agreement with the collective model. If the 4.24 MeV state is assigned to be the first state of a new band with K = 2, magnetic dipole transitions to the K = 0 band should be strongly inhibited, which is in accord with experiment. However, the observed branching ratio of the 4.24 MeV state - which differs from that previously reported by Newton - is much lower than the value of 5, predicted on the collective model. It is also of interest to note that the energies of the ground state band do not accurately follow a JU+I) sequence, but this can be attributed to a vibration-rotation interaction term 2).

50

R. BATCHELOR, A.

J. FERGUSON, H. E. GOVE AND A. E. LITHERLAND

The energy sequence of the ground state band can also be explained if the equilibrium shape of the nucleus is assumed to be a triaxial ellipsoid. From the ratio of the energies of the second and first 2+ states the value of y for magnesium-24, the parameter which determines the deviation of the shape of the nucleus from axial symmetry, is calculated to be 21.9°. Using the detailed calculations of Davydov and Rostovsky 26) the predicted value of the ratio of the energies of the 4+ and 2+ levels is 3, and this agrees very closely with the observed value. According to Davydov and Filippov 10) the predicted branching ratio of the E2 transitions from the 4.24 MeV state and the E2/MI amplitude ratio of the 2.87 MeV radiation on the ellipsoidal model, are given by the following formulae: . 1(4.24) (4.24)5 7 [ 3-2sin 2(3y) ] [9-8 sin 2(3y)] (6) B ranching ratio = --- 1- 1::;=======7 1(2.87) (2.87)5 20 V(9-8 sin2(3y)) sin 2(3y) . E2/Ml amplitude ratio = yO.21 E y eZ R 0 2 80

nCI10gR

(7)

where Ro = ramus of the nucleus, flo = nuclear magneton, and gR = gyromagnetic ratio corresponding to collective motion of the nucleons in the nucleus. From eq. (6) the calculated branching ratio is 0.88, which is lower than the observed value. From eq. (7), taking R o = 1.2 A!x 10- 13 em and gR = Z/A = 0.5, the amplitude ratio is 2. Comparing this with the experimental value of 23, we see that the Ml radiation is more strongly inhibited than is suggested by the model. To summarize, we see that although the levels of Mg24 are in reasonable qualitative accord with a collective model, there are serious quantitative disagreements. From the present work, it is not possible to distinguish between the axially symmetric and asymmetric models. Further information on the higher states will be of considerable interest. The cooperation of Mr. P. G. Ashbaugh and the operating crew of the tandem accelerator is gratefully acknowledged. Note added in proof: It has been pointed out to us by B. R. Mottelson that if one wishes to interpret the branching ratio 1(4.24/1(2.87) in terms of a classification based on rotational bands, one should take into account the mixing between the K = 0 and K = 2 bands. If the admixture of K = 0 into the K = 2 band were only 0.1 % in intensity the observed branching ratio of the 4.24 MeV level can be explained on the reasonable assumption that the B(E2) for a rotational transition K = 0,1 = 2 to K = 0,1 = 0 is about ten times that for the possibly vibrational transition K = 2,1 = 2 to K = 0,1 = O. A similar situation occurs in certain rare earth nuclei 26), in which case general expressions

GAMMA RAYS FROM THE 4.24 MeV STATE IN MAGNESIUM-24

51

for such corrections to E2 branching ratios are given. Mottelson also points out that eq. (7) is incorrect. The model of Davydov and Filippov 10) assumes a single g-factor gR to describe all the degrees of freedom of the nucleus and hence u must point in the same direction as I. This requires that B(Ml) = 0 in eq. (7). However, the K-admixtures permitfinite values for B(MI) since the small admixing of a J( = 2, 1= 2 state into the 1.37 MeV level gives values of B (Ml; K = 2, I = 2' -+ K = 2, 1=2) which are not K-forbidden. Ml transitions of the type K = 0, I = 2' to K = 0, 1= 2 of course do not occur. Using the measured E2/Ml amplitude, the above 0.1 % intensity for band mixing and an intrinsic quadrupole moment of 0.5 X 10-24 em" he obtains /gK-gRI = 0.13 where gK is the g-factor for the intrinsic motion of the K. = 2 band. This interpretation of the observed branching and E2/Ml mixtures for gamma decay of the 4.24 MeV level in Mg 24 could be checked by similar measurements on higher levels in Mg 24 belonging to the K = 2 banel. References 1) P. M. Endt and C. M. Braarns, Revs. Mod. Phys. 29 (1957) 683 2) A. E. Litherland, H. McManus, E. B. Paul, D. A. Bromley and H. E. Gave, Can. J. Phys. 36 (1958) 378 3) P. M. Endt and oJ. C. Kluyver, Revs. Mod. Phys. 26 (1954) 95 4) J. O. Newton, Phys. Rev. 96 (1954) 241 (L); L. Simons, Societ. Scient. Fennicae Commentationes Physico-Mathematicae 13, no. 2 and no. 3 (1959) 5) L. E. Beghian, G. R. Bishop and H. Halban, Phys. Rev. 83 (1951) 186 (L) 6) J. M. Calvert, A. A. Jaffe, A. E. Litherland and E. E. Maslin, Proc, Phys. Soc. A 68 (1955)1008 7) M. El-Wahab, thesis, Alexandria University, Egypt (1956) 8) A. Bohr and B. R. Mottelson, Phys. Rev. 89 (1953) 316 9) P. J. Grant, J. G. Rutherglen, F. C. Flack and G. W. Hutchinson, Proc, Phys. Soc. A 68 (1955) 369 10) A. S. Davydov and G. F. Filippov, Nuclear Physics 8 (1958) 237 11) D. M. van Patter, Bull. Am. Phys, Soc. 4 (1959) 233 12) E. K. Warburton and H. J. Rose, Phys. Rev. 109 (1958) 1199 13) A. E. Litherland and A. J. Ferguson, to be published 14) D. A. Bromley, A. J. Ferguson, H. E. Gove, J. A. Kuehner. A. E. Litherland, E. Almqvist and R. Batchelor, to be published in Can. J. Phys. 15) R. E. Bell. R. Graham and H. E. Petch, Can. J. Phys, 30 (1952) 35 16) F. D. Seward, Phys. Rev. 114 (1959) 514 17) H. E. Gove and A. E. Litherland, Phys. Rev. 113 (1959) 1078 18) M. E. Rose, Phys. Rev. 91 (1953) 610 19) W. T. Sharp, J. M. Kennedy, B. J. Sears and M. G. Hoyle, Chalk River Report No. CRT-556 (1957), Chalk River, Ontario, Canada 20) A. J. Ferguson and A. R. Rutledge, Chalk River Report No. CRP-615 (1957), Chalk River, Ontario, Canada 21) H. E. Gove and A. R. Rutledge, Chalk River Report No. CRP-755 (1958), Chalk River, Ontario, Canada 22) A. R. Rutledge, Chalk River Report No. CRP-851 (1959), Chalk River, Ontario, Canada 23) J. A. M. Cox and H. A. Tolhoek, Physica 19 (1953) 1178 24) S. Devons and L. J. B. Goldfarb, Handbuch der Physik, Vol. 42 (Springer-Verlag 1957) p. 384 25) A. S. Davydov and V. S. Rostovsky, Nuclear Physics 12 (1959) 58 26) Gregers-Hansen, Nielsen and Sheline, Nuclear Physics 12 (1959) 389