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Gamma-ray widths of the 2.21 MeV level in Al27
Nuclear Physics 4 5 (1963) 602----608; ( ~ ) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher
GAMMA-RAY W I D T H S OF T H E 2.21 MeV LEVEL I N A!27 V. J. VANHUYSE and G. J. VANPRAET Natuurkundig Laboratorium, Rijksuniversiteit, Gent, Belgium t Received 29 April 1963 Abstract: The bremsstrahlung spectrum of 2.85 MeV electrons from a linear accelerator has been used to excite the 2.21 MeV level of AI~L From the results of resonance self-absorption we obtained the valued gF' ----(1.8=1=0.4) × 10-2 eV. The angular distribution of the 2.21 MeV resonance radiation was found to be of the form W(O) = 1 q- (0.26=l=0.05)Ps(cos0). The results are interpreted in terms of the collective model.
1. Introduction
In recent years there has been much interest for the nuclei in the ld-2s shell. The properties of these nuclei were interpreted in terms of the collective effects in this shell using the Nilsson model 1). Survey articles were written by Gove 2 ) a n d by Bhatt a). A m o n g other things the striking similarity of the level structure of the nuclei for which the odd particle is 13 was brought to evidence. The lower-lying levels of these nuclei are interpreted as belonging to a K = ~ rotational band based on the ground state and to a K = ½ rotational band based on the first excited state. The level structure of A127 which is one of these nuclei is given in fig. 1. The J~ assignment of the 2.21 MeV level has been the subject of some doubt since some experimental results conflicted with each other 4-6). On the basis of the rotational collective model it was suggested that the 2.21 MeV level was the most likely candidate for the second member (I = 7+) of the ground state rotational band. In recent experiments, Lawergren and Ophel 6) were able to determine a unique spin assignment o f J = 7 by measuring angular distributions and ~,-~, correlations of the Mg 26 (p,),) reaction. Additional information on the collective character of the state can be obtained from the width of the level involved and from the multipole mixing ratio of the transition to the ground state. Metzger et al. 5) have measured the level width using the y-rays from the Mg26(p, y) reaction as a photon source in a resonance fluorescence experiment. They measured also the angular distributions of the resonantly scattered gamma-rays. They favoured a spin ½ for the 2.21 MeV level, the spin value ~ having been ruled out by other experiments. Booth and Wright 7) have done a pure resonance scattering experiment with bremsstrahlung from which they determined the level width with a rather large error. We have measured the mean life of the 2.21 MeV in A127, using a bremsstrahlung spectrum as a photon source. t Work supported by the Belgian lnteruniversity Institute for Nuclear Sciences, Brussels. 602
y-RAY WIDTHSIN A1~7
603
A self-absorption method was applied. We have also measured the angular distribution of the resonance gamma-rays and determined the M1-E2 mixing ratio of the transition.
2. Experimental Procedure For the measurement of the level width, the experimental set-up was about the same as described in a previous paper s). The electron energy of the linear accelerator was 2.85 MeV with a resolution of 3 %. The lead radiator was 0.02 cm thick. The A1 scatterer, which had a thickness of 5.25 g/cm 2 was placed normal to the line bisecting the angle between the incident and scattered beam. The gamma-ray spectrum was detected at a scattering angle of 120 ° by a properly shielded NaI(T1) scintillator (10.2 cm diam. x 10.2 cm) and a gated 128-channel pulse-height analyser. A cylindric collimator in front of the crystal was 25 cm long with a diameter of 4.5 cm. The distance from the target to the detector was 55 cm while a lead absorber of 4 cm was placed just in front of the crystal in order to reduce low energy gamma-rays. As a d u m m y scatterer, natural Mg was used. For the self-absorption measurement the incoming photon beam traversed an A1 absorber of thickness d = 3.00 cm. We define Y~a as the total number of signal counts [(A1 scatt.)-(Mg, scatt.)] per unit monitor response in the channels 0cto/3. Putting the A1 absorber in the primary beam, we measured an attenuated scattered spectrum from which an analogous number Y'p = [(A1 scatt., A1 abs.)-(Mg scatt., no abs.) exp (-aNd)] can be computed, a = 1.85 x 10 -24 cm 2 being the cross section for electronic absorption of gammarays in AI, which is considered constant over the level under investigation, while N is the number of A1 nuclei per cm a. We can express the transmission as f
p,~ --
_ J
OR(E) +
f
{1--exp[--(~R(E)-[-EO.)coNst(~]}exp[--(O.R(E).31-~)Nd ox.
aR(E} + 2~
cos ¢_1 ; O)
in which s(e) --
exp
A
E ( )21 -
(2)
is the Doppler broadened cross section for nuclear resonance fluorescence, g-
2J1 + 1 2Jo+l
is the statistical factor, Jo and J t are the spin values of the ground state and the 2.21 MeV level, respectively, F is the level width, ER is the resonance energy, A is the Doppler width and ~p is the angle formed by the normal to the plane of the scatterer and the incident beam. We have neglected the 2 ~o transitions to other levels than the
604
V, J. V A N H U - Y S E
AND
G. J. V A N P R A E T
ground state. Assuming a Debye temperature 9) 0 = 394 °, the effective temperature 1o) is 320 ° K and A = ER
r2k T, fr']+ L---M-~c2j =
3.28 eV.
(3)
By numerical integration, the theoretical expression (1) was evaluated as a function of gl' so that p(gF) could be plotted. The value of gF associated with the observed transmission can then be determined from that curve. Although a 2.85 MeV brems5*
MeV
zn3
T
221
>90
1.01
i2igs
0St,
2 ½-
11
5*
2 Fig. 1. Scheme of the lower energy levels of AW.
0.2(
Counts per volt o
o
e
01'
:
°°
o o
0.1(
o
XX
o
o
''" 0.0!
~ ~ ~.,, •
0.01
60
Channel number
¢o
8'0
9'0
1~o
Fig. 2. Pulse-height distribution of photons scattered from an AI scatterer and from a Mg scatterer, 0=
120 ° , o - - A P
7, • - - M g .
strahlung spectrum was used, practically no gamma-rays scattered from the 2.73 MeV level were observed, and even if there were some, it is clear from fig. 1 that they could not contribute to the 2.21 MeV transition. Fig. 2 shows the pulse-height
F-RAY WIDTHS IN" A117
605
distribution of the scattered radiation from the A1 and the Mg targets. In order to perform angular distribution measurements, the shielded crystal detector was mounted to rotate about the intersection of the beam and the target so that the angle 0 between the incident beam and the detected gamma-rays could be varied. The 0 = 0 position was determined accurately by measuring the radiation field produced in the lead radiator, for different positions of the detector assembly. The symmetry of the obtained curve checked also that the axis of rotation of the turn-table intersected the beam axis. The angle 0 could be adjusted better than within 0.5 °. The target was rotated for each measurement so that ~o = ½ ( ~ - 0 ) and the error on ~o was also negligible. The distance from the target to the front of the crystal was increased up to 75 cm while the lead absorber was only 3 cm. Pulse-height distributions were measured at angles of 90 °, 105 °, 120 ° and 135 °. The number of resonantly scattered gamma-rays per unit of monitor response in the solid angle dfi under an angle 0 is given by Y,#(O)d~=Kdl"2f(O)f
~_R.(E'
{1 -- exp [ - - ( a . + 2a) cNtq~] }dE ,
(4,
J ~R(E) + :Z#
in which K is a factor independent of 0, containing the geometry, the efficiency of the detector, the bremsstrahlung spectrum, and f ( 0 ) is the value ofthe angular distribution function at the angle 0, while the integral is a measure for the effective target thickness depending on 0 by ¢p and also slightly on the value of gF. It t u r n e d out that for the value of g F obtained by the self-absorption experiment, the integral in (4) took the values 1.00, 0.930, 0.875 and 0.843 at 90 °, 105 °, 120° and 135 °, respectively. Change of F within the experimental errors affects these values less than 0.5%. The different values of the background of non-resonantly scattered gamma-rays had to be taken into account. This background increases considerably when going t o smaller angles, and therefore, no measurements were done at forward angles. At large angles we were limited because of the space needed for the shielding of the detector. 3. Results and Discussion
From the self-absorption measurement the transmission p was determined to be .0.53+0.06 and was found to be practically independent of the choice of ~ and fl in the region of the resonance peak. This p value includes already the factor e -'N~ = 0.716. Comparison with the theoretical curve p ( g F ) yields g F = (1,8_+0.4) x 10- 2 eV. Assuming a spin ½for the 2.21 MeV state, Booth and Wright 7) found from their scattering experiment a mean life x = 3.2 × 10 -14 sec with an estimated error of a b o u t +35 %. This corresponds to a value of g F = 1.37 x 10 -2 eV. The experiment o f Metzger et al. yielded a value g F o = (2.36-+0.30) x 10 -2 eV, a branching ratio F o / F = 0.98 having been taken into account. Within the errors, there is good agreement between the three measurements. The weighted average of the results is g F = (2.05+0.19)x 10 -2 eV. In the further discussion we shall use this value. The
606
V. J. VANHUYSE AND G. J. VANPRAET
result of the angular distribution measurement is given in fig. 3. The solid curve represents a least squares fit o f f ( 0 ) = 1 +A2P2(cos 0) to the data. The value of .42 was found to be (0.26+0.05), which is in complete agreement with the angular distribution of Metzger et al.5), who found once .42 = 0.23+0.03 and with a different scatterer obtained a value A2 = 0.25 +0.07. The weighted mean value of the 1.2
fro)
oe
O 60"
;5 °
165°
90°
120°
1350
'
Fig. 3. Angular distribution of the resonance radiation.
three results is (0.24___0.02). Because of the observed angular distribution, the spin values ½ and ~ are excluded. For a spin ½ the angular distribution should be isotropic while for ~ a function f ( O ) = 1+0.1 P2(cos 0)+0.009P4(cos 0) should be found. The very small branching ratio to the 1.01 MeV and the 0.84 MeV levels makes ½ and ~ rather unlikely. A spin value ~ explains the small branching ratio. Lawergren A2 1.~
~-- ~--~A2 ,~<0
K
A4 0,E
13 ).2
0,~ ,/z.,//1//////// 0.1
,
/ ~
10-4 t0-3 10-2 10-1
,
1
10
~2
102
103
10'4
Fig. 4. Theoretical coefficients o f the P~-terms in the angular distribution function W ( O ) =
1 +AsPs
(cos 0) for mixed dipole-quadrupole resonance radiation for the spin sequence ~ - ~ - ~ .
and Ophel 6) effectively found a unique spin assignment ~ for the considered level by measuring angular distributions and T-7 correlations of the Mg26(p, 7) reaction. Also Towle and Gilboy 11) found a spin -] from neutron scattering studies; they were not able to assign a parity to the level. For a spin-~, one obtains F = (1.51 +_0.14) x 10-2 eV, which corresponds to a mean life z = (2.29+0.21)x 10 -14 sec. Fig. 4 gives the coefficients of P2(cos 0) and P4(cos 0) for a spin sequence ~-~-~ s ~ s as a function
~,-RAY WIDTHS IN A12~
607
of the mixing ratio 62 of the transition. For 6 < 0 one finds 62 = (0.8+0.2) x l0 -3 while for 6 > 0, the result is 62 = 0.23+0.02. For odd parity of the ½ level one finds as a lower limit 62 = 0.6 × 10 -3 which yields a partial width F ( M 2 ) = 0 . 9 × 10 -5 eV. This should mean an enhancement by a factor of at least 80, which would be rather unusual. Even parity for the 2.21 MeV level makes the level a very probable analogue of the 1.61 MeV ½+ states in A125 and Mg 2s, the second members of the ground state rotational band. This implies a positive sign for the mixing amplitude 12), the sign of 6 being the same as the sign of gK--gR/Qo, in which Qo is the intrinsic quadrupole moment of the nucleus, g~ and gR are the gyromagnetic ratios of the intrinsic and collective motion. Thus one has finally 62 = (0.23+0.02). This leads to the partial width F(M1) = (1.22+0.12) x 10 -2 eV and F(E2)--- (2.9_+0.45) x 10 -3 eV, which corresponds to the reduced transition probabilities B(M1; ½--,-~)------(1.1 +_0.1) x l0 -29 e 2. cm 2 and B(E2; ½ ~ -~)= (6.4_+ 1.0) x l0 - s l e 2. cm 4. Taking the nuclear radius R = 1.2 A ~ fro, the single particle units for the reduced transition probabilities are B(M1)sp = 2.0 x 10 -2s e 2. cm 2 and B(E2)s p = 4.9 x l0 -s2 e 2. cm 4. For the E2 transition, the enhancement factor is then 14. Considering the 2.21 MeV level as the first excited member of the ground state rotational band, we find for the interband transition 13) B(M1; -] ~ ~-)c = 7.3 x l0 -29 e 2. cm2; for ga and g2, the values 1.92 and 0.48 were used. McManus and Sharp have derived a generalized expression for the reduced E2 transition probability, based on the Nilsson model. This formula ~3) in which the Nilsson notation is used simplifies in our case to the form
B(E2; I --, I') = ~
~
G2E2I(I2KK'-- KII'K')(I + Y~.2)]2
(5)
The parameter Y~2 contains the collective contribution and is given by Y~2 =
xZA ~
r](l +~-6) E
GE2
(N'l'lllNl)6~r6xr'atAa;A',
(6)
IA
~/ and c~ being the spheroidicity parameters and x the coupling parameter; the atA are the normalized Nilsson eigenfunction coefficients. To a very good approximation m/ = 6. In our case GE2 = -- 1 and the sum ~ a factor equals 1. For the oscillator level spacing, the usual estimate hco o = 41A -~ MeV is used. The deformation parameter 6 was determined from the relation
Oo = ,-~n~ ZR2fl(I +0.16fl),
(7)
where fl = 1.06 6 and the root mean square radius R = ro A~. The 'factor ro was found to be 1.36 fm from electron scattering experiments ~4). I f there is no band mixing, the relation between the observed and the intrinsic quadrupole moment Qo is 3K 2-I(I+I)Q .
Qo,,-
i3 o,
608
V. J'. VANHUYSE AND O. I. VANPRAET
this gives a value Qo = 0.42 x 1 0 - ' cm 24 corresponding to Qob, = 0.15 x 10 -24 c m 2. One finds then an estimate for the deformation 6 = 0.233. Finally we obtain for eq. (5) B(E2, ~ --, ~) = l l . T x 10 -21 e 2. cm 4. We consider the agreement between the experimental values and the rotational model predictions as satisfying. The results o f the present experiment thus seem to give additional support for the validity o f the Nilsson model for the nucleus A12~. References 1) S. G. Nilsson, Mat. Fys. Medd. Dan. Vid. Selsk. 29, No. 16 (1955) 2) H. E. Gore, Proc. Int. Conf. on Nuclear Structure (University of Toronto Press, Toronto, 1960) p. 451 3) K. H. Bhatt, Nuclear Physics 39 (1962) 375 4) C. Van der Leun et al., Physica 22 (1956) 1223 5) F. R. Metzger, C. P. Swarm and V. K. Rasmussen, Nuclear Physics 16 (1960) 568 6) B. T. Lawergren and T. R. Ophel, Phys. Lett. 2 (1962) 265 7) E. C. Booth and K. A. Wright, Nuclear Physics 35 (1962) 472 8) V. J. Vanhuyse and G. J. Vanpraet, Nuclear Physics 43 (1963) 344 9) J. deLaunay, Solid state physics, ed. by F. Seitz e t aL (Academic Press, New York, 1956) Vol. 2, p. 233 10) W. Lamb, Phys. Rev. 55 (1939) 190 11 ) J. H. Towle and W. B. Gilboy, Nuclear Physics 39 (1962) 300 12) K. Alder et al., Revs. Mod. Phys. 28 (1956) 432 13) D. A. Bromley et al., Can. J. Phys. 35 (1957) 1057 14) R. Lombard, G. R. Bishop and B. Milman, Rappr. LAL 1022, Orsay 15) A. Bohr and B. R. Mottelson, Mat. FYS. Medd. Dan. Vid. Selsk. 27, No. 16 (1953)
GAMMA-RAY W I D T H S OF T H E 2.21 MeV LEVEL I N A!27 V. J. VANHUYSE and G. J. VANPRAET Natuurkundig Laboratorium, Rijksuniversiteit, Gent, Belgium t Received 29 April 1963 Abstract: The bremsstrahlung spectrum of 2.85 MeV electrons from a linear accelerator has been used to excite the 2.21 MeV level of AI~L From the results of resonance self-absorption we obtained the valued gF' ----(1.8=1=0.4) × 10-2 eV. The angular distribution of the 2.21 MeV resonance radiation was found to be of the form W(O) = 1 q- (0.26=l=0.05)Ps(cos0). The results are interpreted in terms of the collective model.
1. Introduction
In recent years there has been much interest for the nuclei in the ld-2s shell. The properties of these nuclei were interpreted in terms of the collective effects in this shell using the Nilsson model 1). Survey articles were written by Gove 2 ) a n d by Bhatt a). A m o n g other things the striking similarity of the level structure of the nuclei for which the odd particle is 13 was brought to evidence. The lower-lying levels of these nuclei are interpreted as belonging to a K = ~ rotational band based on the ground state and to a K = ½ rotational band based on the first excited state. The level structure of A127 which is one of these nuclei is given in fig. 1. The J~ assignment of the 2.21 MeV level has been the subject of some doubt since some experimental results conflicted with each other 4-6). On the basis of the rotational collective model it was suggested that the 2.21 MeV level was the most likely candidate for the second member (I = 7+) of the ground state rotational band. In recent experiments, Lawergren and Ophel 6) were able to determine a unique spin assignment o f J = 7 by measuring angular distributions and ~,-~, correlations of the Mg 26 (p,),) reaction. Additional information on the collective character of the state can be obtained from the width of the level involved and from the multipole mixing ratio of the transition to the ground state. Metzger et al. 5) have measured the level width using the y-rays from the Mg26(p, y) reaction as a photon source in a resonance fluorescence experiment. They measured also the angular distributions of the resonantly scattered gamma-rays. They favoured a spin ½ for the 2.21 MeV level, the spin value ~ having been ruled out by other experiments. Booth and Wright 7) have done a pure resonance scattering experiment with bremsstrahlung from which they determined the level width with a rather large error. We have measured the mean life of the 2.21 MeV in A127, using a bremsstrahlung spectrum as a photon source. t Work supported by the Belgian lnteruniversity Institute for Nuclear Sciences, Brussels. 602
y-RAY WIDTHSIN A1~7
603
A self-absorption method was applied. We have also measured the angular distribution of the resonance gamma-rays and determined the M1-E2 mixing ratio of the transition.
2. Experimental Procedure For the measurement of the level width, the experimental set-up was about the same as described in a previous paper s). The electron energy of the linear accelerator was 2.85 MeV with a resolution of 3 %. The lead radiator was 0.02 cm thick. The A1 scatterer, which had a thickness of 5.25 g/cm 2 was placed normal to the line bisecting the angle between the incident and scattered beam. The gamma-ray spectrum was detected at a scattering angle of 120 ° by a properly shielded NaI(T1) scintillator (10.2 cm diam. x 10.2 cm) and a gated 128-channel pulse-height analyser. A cylindric collimator in front of the crystal was 25 cm long with a diameter of 4.5 cm. The distance from the target to the detector was 55 cm while a lead absorber of 4 cm was placed just in front of the crystal in order to reduce low energy gamma-rays. As a d u m m y scatterer, natural Mg was used. For the self-absorption measurement the incoming photon beam traversed an A1 absorber of thickness d = 3.00 cm. We define Y~a as the total number of signal counts [(A1 scatt.)-(Mg, scatt.)] per unit monitor response in the channels 0cto/3. Putting the A1 absorber in the primary beam, we measured an attenuated scattered spectrum from which an analogous number Y'p = [(A1 scatt., A1 abs.)-(Mg scatt., no abs.) exp (-aNd)] can be computed, a = 1.85 x 10 -24 cm 2 being the cross section for electronic absorption of gammarays in AI, which is considered constant over the level under investigation, while N is the number of A1 nuclei per cm a. We can express the transmission as f
p,~ --
_ J
OR(E) +
f
{1--exp[--(~R(E)-[-EO.)coNst(~]}exp[--(O.R(E).31-~)Nd ox.
aR(E} + 2~
cos ¢_1 ; O)
in which s(e) --
exp
A
E ( )21 -
(2)
is the Doppler broadened cross section for nuclear resonance fluorescence, g-
2J1 + 1 2Jo+l
is the statistical factor, Jo and J t are the spin values of the ground state and the 2.21 MeV level, respectively, F is the level width, ER is the resonance energy, A is the Doppler width and ~p is the angle formed by the normal to the plane of the scatterer and the incident beam. We have neglected the 2 ~o transitions to other levels than the
604
V, J. V A N H U - Y S E
AND
G. J. V A N P R A E T
ground state. Assuming a Debye temperature 9) 0 = 394 °, the effective temperature 1o) is 320 ° K and A = ER
r2k T, fr']+ L---M-~c2j =
3.28 eV.
(3)
By numerical integration, the theoretical expression (1) was evaluated as a function of gl' so that p(gF) could be plotted. The value of gF associated with the observed transmission can then be determined from that curve. Although a 2.85 MeV brems5*
MeV
zn3
T
221
>90
1.01
i2igs
0St,
2 ½-
11
5*
2 Fig. 1. Scheme of the lower energy levels of AW.
0.2(
Counts per volt o
o
e
01'
:
°°
o o
0.1(
o
XX
o
o
''" 0.0!
~ ~ ~.,, •
0.01
60
Channel number
¢o
8'0
9'0
1~o
Fig. 2. Pulse-height distribution of photons scattered from an AI scatterer and from a Mg scatterer, 0=
120 ° , o - - A P
7, • - - M g .
strahlung spectrum was used, practically no gamma-rays scattered from the 2.73 MeV level were observed, and even if there were some, it is clear from fig. 1 that they could not contribute to the 2.21 MeV transition. Fig. 2 shows the pulse-height
F-RAY WIDTHS IN" A117
605
distribution of the scattered radiation from the A1 and the Mg targets. In order to perform angular distribution measurements, the shielded crystal detector was mounted to rotate about the intersection of the beam and the target so that the angle 0 between the incident beam and the detected gamma-rays could be varied. The 0 = 0 position was determined accurately by measuring the radiation field produced in the lead radiator, for different positions of the detector assembly. The symmetry of the obtained curve checked also that the axis of rotation of the turn-table intersected the beam axis. The angle 0 could be adjusted better than within 0.5 °. The target was rotated for each measurement so that ~o = ½ ( ~ - 0 ) and the error on ~o was also negligible. The distance from the target to the front of the crystal was increased up to 75 cm while the lead absorber was only 3 cm. Pulse-height distributions were measured at angles of 90 °, 105 °, 120 ° and 135 °. The number of resonantly scattered gamma-rays per unit of monitor response in the solid angle dfi under an angle 0 is given by Y,#(O)d~=Kdl"2f(O)f
~_R.(E'
{1 -- exp [ - - ( a . + 2a) cNtq~] }dE ,
(4,
J ~R(E) + :Z#
in which K is a factor independent of 0, containing the geometry, the efficiency of the detector, the bremsstrahlung spectrum, and f ( 0 ) is the value ofthe angular distribution function at the angle 0, while the integral is a measure for the effective target thickness depending on 0 by ¢p and also slightly on the value of gF. It t u r n e d out that for the value of g F obtained by the self-absorption experiment, the integral in (4) took the values 1.00, 0.930, 0.875 and 0.843 at 90 °, 105 °, 120° and 135 °, respectively. Change of F within the experimental errors affects these values less than 0.5%. The different values of the background of non-resonantly scattered gamma-rays had to be taken into account. This background increases considerably when going t o smaller angles, and therefore, no measurements were done at forward angles. At large angles we were limited because of the space needed for the shielding of the detector. 3. Results and Discussion
From the self-absorption measurement the transmission p was determined to be .0.53+0.06 and was found to be practically independent of the choice of ~ and fl in the region of the resonance peak. This p value includes already the factor e -'N~ = 0.716. Comparison with the theoretical curve p ( g F ) yields g F = (1,8_+0.4) x 10- 2 eV. Assuming a spin ½for the 2.21 MeV state, Booth and Wright 7) found from their scattering experiment a mean life x = 3.2 × 10 -14 sec with an estimated error of a b o u t +35 %. This corresponds to a value of g F = 1.37 x 10 -2 eV. The experiment o f Metzger et al. yielded a value g F o = (2.36-+0.30) x 10 -2 eV, a branching ratio F o / F = 0.98 having been taken into account. Within the errors, there is good agreement between the three measurements. The weighted average of the results is g F = (2.05+0.19)x 10 -2 eV. In the further discussion we shall use this value. The
606
V. J. VANHUYSE AND G. J. VANPRAET
result of the angular distribution measurement is given in fig. 3. The solid curve represents a least squares fit o f f ( 0 ) = 1 +A2P2(cos 0) to the data. The value of .42 was found to be (0.26+0.05), which is in complete agreement with the angular distribution of Metzger et al.5), who found once .42 = 0.23+0.03 and with a different scatterer obtained a value A2 = 0.25 +0.07. The weighted mean value of the 1.2
fro)
oe
O 60"
;5 °
165°
90°
120°
1350
'
Fig. 3. Angular distribution of the resonance radiation.
three results is (0.24___0.02). Because of the observed angular distribution, the spin values ½ and ~ are excluded. For a spin ½ the angular distribution should be isotropic while for ~ a function f ( O ) = 1+0.1 P2(cos 0)+0.009P4(cos 0) should be found. The very small branching ratio to the 1.01 MeV and the 0.84 MeV levels makes ½ and ~ rather unlikely. A spin value ~ explains the small branching ratio. Lawergren A2 1.~
~-- ~--~A2 ,~<0
K
A4 0,E
13 ).2
0,~ ,/z.,//1//////// 0.1
,
/ ~
10-4 t0-3 10-2 10-1
,
1
10
~2
102
103
10'4
Fig. 4. Theoretical coefficients o f the P~-terms in the angular distribution function W ( O ) =
1 +AsPs
(cos 0) for mixed dipole-quadrupole resonance radiation for the spin sequence ~ - ~ - ~ .
and Ophel 6) effectively found a unique spin assignment ~ for the considered level by measuring angular distributions and T-7 correlations of the Mg26(p, 7) reaction. Also Towle and Gilboy 11) found a spin -] from neutron scattering studies; they were not able to assign a parity to the level. For a spin-~, one obtains F = (1.51 +_0.14) x 10-2 eV, which corresponds to a mean life z = (2.29+0.21)x 10 -14 sec. Fig. 4 gives the coefficients of P2(cos 0) and P4(cos 0) for a spin sequence ~-~-~ s ~ s as a function
~,-RAY WIDTHS IN A12~
607
of the mixing ratio 62 of the transition. For 6 < 0 one finds 62 = (0.8+0.2) x l0 -3 while for 6 > 0, the result is 62 = 0.23+0.02. For odd parity of the ½ level one finds as a lower limit 62 = 0.6 × 10 -3 which yields a partial width F ( M 2 ) = 0 . 9 × 10 -5 eV. This should mean an enhancement by a factor of at least 80, which would be rather unusual. Even parity for the 2.21 MeV level makes the level a very probable analogue of the 1.61 MeV ½+ states in A125 and Mg 2s, the second members of the ground state rotational band. This implies a positive sign for the mixing amplitude 12), the sign of 6 being the same as the sign of gK--gR/Qo, in which Qo is the intrinsic quadrupole moment of the nucleus, g~ and gR are the gyromagnetic ratios of the intrinsic and collective motion. Thus one has finally 62 = (0.23+0.02). This leads to the partial width F(M1) = (1.22+0.12) x 10 -2 eV and F(E2)--- (2.9_+0.45) x 10 -3 eV, which corresponds to the reduced transition probabilities B(M1; ½--,-~)------(1.1 +_0.1) x l0 -29 e 2. cm 2 and B(E2; ½ ~ -~)= (6.4_+ 1.0) x l0 - s l e 2. cm 4. Taking the nuclear radius R = 1.2 A ~ fro, the single particle units for the reduced transition probabilities are B(M1)sp = 2.0 x 10 -2s e 2. cm 2 and B(E2)s p = 4.9 x l0 -s2 e 2. cm 4. For the E2 transition, the enhancement factor is then 14. Considering the 2.21 MeV level as the first excited member of the ground state rotational band, we find for the interband transition 13) B(M1; -] ~ ~-)c = 7.3 x l0 -29 e 2. cm2; for ga and g2, the values 1.92 and 0.48 were used. McManus and Sharp have derived a generalized expression for the reduced E2 transition probability, based on the Nilsson model. This formula ~3) in which the Nilsson notation is used simplifies in our case to the form
B(E2; I --, I') = ~
~
G2E2I(I2KK'-- KII'K')(I + Y~.2)]2
(5)
The parameter Y~2 contains the collective contribution and is given by Y~2 =
xZA ~
r](l +~-6) E
GE2
(N'l'lllNl)6~r6xr'atAa;A',
(6)
IA
~/ and c~ being the spheroidicity parameters and x the coupling parameter; the atA are the normalized Nilsson eigenfunction coefficients. To a very good approximation m/ = 6. In our case GE2 = -- 1 and the sum ~ a factor equals 1. For the oscillator level spacing, the usual estimate hco o = 41A -~ MeV is used. The deformation parameter 6 was determined from the relation
Oo = ,-~n~ ZR2fl(I +0.16fl),
(7)
where fl = 1.06 6 and the root mean square radius R = ro A~. The 'factor ro was found to be 1.36 fm from electron scattering experiments ~4). I f there is no band mixing, the relation between the observed and the intrinsic quadrupole moment Qo is 3K 2-I(I+I)Q .
Qo,,-
i3 o,
608
V. J'. VANHUYSE AND O. I. VANPRAET
this gives a value Qo = 0.42 x 1 0 - ' cm 24 corresponding to Qob, = 0.15 x 10 -24 c m 2. One finds then an estimate for the deformation 6 = 0.233. Finally we obtain for eq. (5) B(E2, ~ --, ~) = l l . T x 10 -21 e 2. cm 4. We consider the agreement between the experimental values and the rotational model predictions as satisfying. The results o f the present experiment thus seem to give additional support for the validity o f the Nilsson model for the nucleus A12~. References 1) S. G. Nilsson, Mat. Fys. Medd. Dan. Vid. Selsk. 29, No. 16 (1955) 2) H. E. Gore, Proc. Int. Conf. on Nuclear Structure (University of Toronto Press, Toronto, 1960) p. 451 3) K. H. Bhatt, Nuclear Physics 39 (1962) 375 4) C. Van der Leun et al., Physica 22 (1956) 1223 5) F. R. Metzger, C. P. Swarm and V. K. Rasmussen, Nuclear Physics 16 (1960) 568 6) B. T. Lawergren and T. R. Ophel, Phys. Lett. 2 (1962) 265 7) E. C. Booth and K. A. Wright, Nuclear Physics 35 (1962) 472 8) V. J. Vanhuyse and G. J. Vanpraet, Nuclear Physics 43 (1963) 344 9) J. deLaunay, Solid state physics, ed. by F. Seitz e t aL (Academic Press, New York, 1956) Vol. 2, p. 233 10) W. Lamb, Phys. Rev. 55 (1939) 190 11 ) J. H. Towle and W. B. Gilboy, Nuclear Physics 39 (1962) 300 12) K. Alder et al., Revs. Mod. Phys. 28 (1956) 432 13) D. A. Bromley et al., Can. J. Phys. 35 (1957) 1057 14) R. Lombard, G. R. Bishop and B. Milman, Rappr. LAL 1022, Orsay 15) A. Bohr and B. R. Mottelson, Mat. FYS. Medd. Dan. Vid. Selsk. 27, No. 16 (1953)