positive-parity bands in 29 si
TRANSCRIPT
Positive-Parity Bands in ' Si
A. A. PILT', R. H. SPEAR', R. V. ELLIOTT~, AND J. A. KUEHNER Tandem Accelerator Laboratory, McMaster University, Hamilton, Ontario
Received December 17, 1970
A study has been made of several high spin members of the ground state ( K n = 1/2+) and first-excited state ( K n = 3 / 2 + ) rotational bands in the presumed oblate nucleus 19Si. Gamma-ray angular distribution and linear polarization measurements have confirmed the spin and parity of the 4081 keV level to be 7 / 2 + , and levels at 4742 and 5283 keV have been shown to have Jn = 9 / 2 + and ( 7 / 2 + , 3 / 2 + ) respectively. Branching and mixing ratios for the transitions from these states have also been determined; in con- junction with previously measured lifetimes, transition strengths are calculated. The results are compared with the predictions of a Nilsson-model calculation including the effects of coriolis mixing of the low-lying positive parity bands.
On a etudit plusieurs termes de spins ClevCs des bandes de rotation du niveau fondamental (K" = 1!2+) et du premier Ctat excitC ( K n = 3 / 2 + ) du noyau lgSi prCsumC aplati. Les mesures de distribution angu- laire et de polarisation rectiligne du rayonnement gamma ont confirme que le spin et la parite du niveau ?t 4081 keV sont 7 / 2 + . On a aussi montrt que les niveaux ?t 4742 et 5283 keV ont J" = 912' et ( 7 / 2 + , 312) respectivement. Les rapports de branchement et de mClange pour les transitions issues de ces etats ont aussi Cte dCterminCs; en conjonction avec les vies moyennes mesurkes prCcCdemment, les forces de transition sont calculees. Les rksultats sont comparCs avec les predictions de calculs basts sur un modkle de Nilsson incluant les effets de melanges de coriolis de bandes possidant une faible polarite positive.
Canadian Journal of Physics, 49, 1263 (1971)
1. Introduction nucleus. An earlier publication (Spear et al. 1971)
~ l . , ~ nuclei in the mass region 27-29 are of was devoted to a possible rotational band based
particular interest because of the current evidence On the 3.623 MeV level. It was shown 'On-
(see, for example, Hirko 1969) that the nuclear c l u ~ i v e l ~ by linear polarization and angular dis-
deformation changes from prolate to oblate near tribution measurements that the and parity
this part of the 2s-ld shell. Although the proper- the 3.623 MeV level were 7/2- and arguments
ties of the low-lying states of most nuclei in this were given to indicate that a level at 5.255 MeV
region are quite well known (Endt and van der has Jn = 912-, in agreement with the work of
Leun 1967), attempts to describe them in the light Bardin et (lg70).
of one of the current nuclear models have proven This paper is devoted to the study Of the to be rather unsatisfactory, In particular, the electromagnetic properties of high-spin members
great success of the ~i~~~~~ model in explaining of the possible positive-parity rotational bands
the properties of 2sMg and 2 5 ~ ~ has not been that may exist, in particular those based on the
reproduced in this mass region, despite the fact ground state (Kn = 'I2+) and MeV state
that Z9Si is known to be deformed (Hirko 1969). (Kn = 312') of "Si, in an attempt to improve
~ ~ ~ ~ ~ ~ h ~ l ~ ~ ~ , it appears that the Nilsson model the understanding of this nucleus in the light of
is a promising approach, although a core ex- the Nilsson model predictions. Of particular
citation model (castel et 1970) is also con- interest is the study of y-ray transitions within
sistent with much of the experimental evidence; and between these bands, for a study Of the accordingly, we have embarked on a study of electromagnetic transition strengths may indicate
high-spin states in 29si which may be assigned to what extent coriolis mixing is important in the
to various rotational bands based on either the description Of the states Of 29Si.
ground state or one of the excited states of this 1" a study of this it is to sure level parities, since both positive and
'Holder of a National Research Council Postgraduate negative parity levels are predicted to be present Scholarship. by both the Nilsson model and the core-excitation
'Permanent address: Department of Nuclear Physics, Australian National University, Canberra, A.C.T., The measurement o f ~ - r a ~ linear polariza- Australia. tions in conjunction with y-ray angular dis-
3 N o ~ at Ontario Hydro Ltd., Toronto, Ontario. tributions yields, in many cases, unambiguous
Can
. J. P
hys.
Dow
nloa
ded
from
ww
w.n
rcre
sear
chpr
ess.
com
by
UN
IV W
IND
SOR
on
11/1
4/14
For
pers
onal
use
onl
y.
1264 CANADIAN JOURNAL OF PHYSICS. VOL. 49, 1971
spin and parity assignments as well as sharp limits on the multipole mixing ratios associated with the decay of these levels. Other methods used for determining level parities, in particular the study of angular distributions of particles following transfer reactions, rely on the theory of direct reactions. This is rather unsatisfactory, especially if more than one particle is transferred, because of uncertainties in the theory. For light nuclei, moreover, one frequently finds large non-direct reaction amplitudes, leading to further uncertain- ties. The study of y-ray linear polarizations, how- ever, does not depend on the mechanism of the reaction producing the final state, but only on the well known quantum-mechanical theory of radiation (e.g. Rose and Brink 1967), and thus leads to parity assignments with a large measure of confidence.
2. Experimental Procedure The 26Mg(a,ny)29Si reaction was used to
produce "Si nuclei in their excited states. Spins and parities of the levels and multipole mixing ratios of the y transitions were obtained by analyzing the results of y-ray angular distribution and linear polarization measurements. Because the Q value of the 26Mg(a, n)29Si reaction is only 36 keV, a suitable choice of incident a-particle energy leads to near-threshold population of the states of 29Si of interest. With an incident channel spin of 0 and low orbital angular momentum of the emitted neutrons, only the lowest magnetic substates of these levels will be populated. The resulting strong alignment ensures in favorable cases that the y-ray angular distribution will be anisotropic and that the linear polarization will be nonzero.
The 26Mg targets were prepared by vacuum evaporation of MgO enriched to 299% in 26Mg onto a tantalum backing 0.010 in. thick. Lan- thanum metal was added to the MgO in stoi- chiometric proportions as a reducing agent during the evaporation. Several successive evaporations onto the same substrate were required to obtain targets of the desired thickness (about 200 pg/ cm2).
The McMaster University tandem accelerator was used to produce the 5.54 and 6.30 MeV helium ion beams, collimated to - 1 mm2 at the target position by a tantalum aperture located approximately 25 mm away from the target. The beam current was kept below - 1 pA of He++ ions to minimize target deterioration.
The resulting y rays were detected with an array of three Ge(Li) spectrometers. A 40 cm3 coaxial detector with a resolution (FWHM) at 1.332 MeV of 3 keV was used to measure the y-ray angular distributions in the angular range from 0" to 90" to the incoming beam. A second large detector with somewhat poorer resolution (5.5 keV) was placed at 135" to the beam and served as a monitor counter. Finally, a small planar crystal of dimensions 6 x 3.5 x 0.65 cm and resolution 4.5 keV was used as a Compton polarimeter placed at 90" to the beam opposite the angular distribution detector.
The operation of such a polarimeter has been described by Ewan et al. (1969) and Litherland et al. (1970); however, we give here a brief description for completeness. The detection of polarization makes use of the fact that Compton scattering of the y ray incident on the crystal is maximum in the plane perpendicular to the elec- tric vector. Since for E, 2 500 keV the major contribution to the full energy peak of a Ge(Li) detector arises from events where the incident y rays are first Compton scattered and then totally absorbed in the crystal, a thin planar detector will have a higher yield in the full energy peak with the electric vector perpendicular to the plane of the detector than with it parallel. Con- sequently, a measurement of the full energy yield with the plane of the detector first parallel and then perpendicular, respectively, to the reaction plane will yield information on the degree of linear polarization of the radiation. Writing the respective yields as N, , and N,, the experimental asymmetry is given by
Introducing the detector sensitivity R, which is the observed asymmetry for a y ray completely polarized perpendicular to the reaction plane, the measured polarization is then given by
The sensitivity R of the detector used has been measured for a number of y-ray energies by Baxter et al. (1970); an additional point on the curve was obtained from the polarization of the 2028 keV pure E2 y ray in 29Si (R = 0.08 $. 0.02) and was in good agreement with the previously determined points. A Monte Carlo calculation (Lam 1970) indicates that the sensitivity falls from -0.08 at 2 MeV to -0.05 for 4 to 5 MeV
Can
. J. P
hys.
Dow
nloa
ded
from
ww
w.n
rcre
sear
chpr
ess.
com
by
UN
IV W
IND
SOR
on
11/1
4/14
For
pers
onal
use
onl
y.
PlLT ET AL.: POSITIVE-PARITY BANDS IN 2% 1265
y rays. Thus the experimental asymmetry, even as the intensity. This procedure was used to for completely polarized y rays, is quite small. obtain the areas of ally rays of interest recorded
The data were recorded in 8172 channels of a in the angular distribution, polarization, and two Nuclear Data 3300 analyzer operating in a mode monitor spectra. such that the first 4096 channels contained the Because there is no well-known spin 112 state angular distribution and monitor spectra and the (other than the ground state) in 29Si, normaliza- second 4096 channels contained the polarimeter tion cannot be done internally. The consequent and monitor spectra. Such a configuration re- sulted in the possibility of independent accumu- lation of the two sets of 4096 channel spectra. Input events and stored events were scaled allow- ing dead times for all spectra to be accurately measured.
Angular distribution spectra were accumulated for approximately 1 h periods. A total of three spectra were measured at each of the angles 0, 20.7, 30, 37.8, 45, 52.2, 60, 69.3, and 90 degrees, corresponding to equal intervals of cos20. Polarimeter spectra, because of the reduced effi- ciency of the small crystal, were collected for approximately 3 h periods at each orientation (parallel and perpendicular), the crystal being rotated once for each measurement of three angles with the movable detector. A total of three spectra at each orientation were taken. All spectra were dumped on magnetic tape for analysis following each run.
The alignment of the correlation table was determined at the end of the experiment using the strong 1.273 MeV y ray in 29Si resulting from the decay of 6.5 min 29A1 produced by the 2 6 ~ g ( a , p)29A1 reaction. The target was irradiated for approximately 10 min periods after which the beam was turned off and spectra collected during the following 10 min at several angles. The resulting angular distribution normalized to the fixed monitor counter was isotropic to within 2%.
3. Analysis of Data
It was mentioned in Section 2 that experimental asymmetries observed in the polarization were typically quite small (58%). Consequently, if accurate values of the y-ray linear polarizations are to be extracted, the intensities of the full energy peaks must be carefully measured. Of particular importance is the determination of
necessity of using a monitor detector leaves open the possibility of certain systematic errors due to such effects as misalignments in the geometry and wandering of the beam spot on the target. Errors due to these are difficult to estimate but the consistency of both the angular distribution and polarization data after other corrections had been made indicates that they were very small. Consequently, y-ray yields were normalized to the strong 2028 keV gamma ray resulting from the decay of the second excited state in 29Si as de- tected in the monitor counter. This state is rather weakly fed (-4%) in the P decay of 29Al which is produced in the very weakly competing 2 6 ~ g ( a , P)'~AI reaction (Jones et al. 1970) and hence the presence of the resulting 2028 keV y rays is not expected to confound the results appreciably. The normalized y-ray angular distribution data were corrected for attenuation in the target backing and for the finite solid angle effects. A small correction to the polarization asymmetry resulting from the y-ray angular distribution was also made.
The level parameters and y-ray multipole mixing ratios were obtained from the angular distribution and polarization data using a modi- fied version of a program described by Twin et al. (1970). For specified initial and final spins, parity change, and multipole mixing ratio 6 a grid search among the substate populations P(m) of the initial state was carried out to find the combina- tion minimizing x2 of the combined angular distribution and polarization fit. In addition to the usual requirement
further restrictions on the population parameters were estimated from the predictions of the
background. A modified version of a nonlinear statistical model. witha-particle energies suitably least squares fitting subroutine (Hay 1969) was chosen, the final state of interest is populated used to fit the region of each peak in the spectra near threshold. This results in primarily s-wave of interest to a skew-Gaussian peak shape super- neutrons being emitted and consequent alignment imposed on background taken to be the sum of of the final state such that one expects P(1/2) >> an exponential and a linear function. The fitted P(3/2). A Hauser-Feshbach calculation allows area of the peak less the background was taken an estimate of the magnitudes of the population
Can
. J. P
hys.
Dow
nloa
ded
from
ww
w.n
rcre
sear
chpr
ess.
com
by
UN
IV W
IND
SOR
on
11/1
4/14
For
pers
onal
use
onl
y.
1266 CANADIAN JOURNAL OF PHYSICS. VOL. 49, 1971
TABLE 1. Listed are Legendre coefficients, corrected for solid angle effects, fitted to angular distributions of y-ray deexciting levels in 29Si, and the polarization for each y ray. The definition of polarization used is
given in the text; P = + 1 corresponds to a fully polarized y ray;P = 0 to no polarization
Incident Transition Legendre coefficients energy Initial Final energy Polarization (MeV) state state (MeV) az k Aaz a, k Pf AP
parameters; for the reaction and energies of interest here, we find P(1/2) - 0.8, P(3/2) -- 0.15, P(5/2) -- 0.05. The effects of fluctuations (see, for example, Ericson 1963), however, complicate this simple picture. From a knowledge of the target thickness and coherence width of the com- pound nucleus, these fluctuations and their effect on the population parameters can be estimated. In the present experiment, fluctuations in the order of at least 30% are expected. Accordingly in the grid search over the population parameters, the ratio P(3/2)/P(1/2) was allowed to vary from 0.0 to 0.8 and P(5/2)/P(1/2) from 0.0 to 0.3, thus encompassing a considerably greater range than that expected by the calculation. This search was carried out for all possible spin values of the initial state for several values of F to obtain the usual x2 us. arctan 6 plots for various spin hypotheses. Only those solutions were accepted for which X2 was less than the 0.1% limit.
4. Results
The experimental data for the 29Si gamma rays studied in this work are summarized in Table 1. For each y ray, the values of a, and a, obtained from a least-squares fit of the angular distribution data to a Legendre polynomial expansion
are given; the polarization of the corresponding r ray is shown in the last column. The corrections described in Section 3 have been applied to the angular distribution and polarization data.
The remainder of this section is devoted to a discussion of the results obtained for they transi- tions from the levels at 4081,4742, and 5283 keV. The excitation energies given are obtained from a weighted average of (1) results obtained in the present work, (2) energies given by Endt and van der Leun (1967), and (3) values obtained by Meyer-Schiitzmeister et al. (1969) using the
FIG. 1. Energy levels and decay of 29Si for E, 5 5.3 MeV. The method of assigning excitation energies is discussed in the text; the errors are believed to be < 3 keV in all cases. The spins, parities, and decay modes for the states at 4081, 4742, and 5283 keV have been determined in the present work; those for the 3623 and 5255 keV states in a previous publication (Spear et al. 1971) and those for the remaining have been extracted from the compilation of Endt and van der Leun (1967) and references therein.
27A1(3He, P)29Si reaction. Figure 1 shows a level scheme of 29Si incorporating both previous and new results.
4.1 The 4081 ke V Level The only spin assignment to this state existing
in the literature appears to be that of Ferguson et al. (1967), who assign J = 712 from the results ofa 29Si(pp'yy) angular correlation measurement.
Becker et al. (1967) measured the particle- gamma angular correlation from 28Si(d, py)29Si reaction but were unable to reach any conclusion other than J 2 312. A recent remeasurement of the 29Si(p, pry) angular correlation (Main et al.
Can
. J. P
hys.
Dow
nloa
ded
from
ww
w.n
rcre
sear
chpr
ess.
com
by
UN
IV W
IND
SOR
on
11/1
4/14
For
pers
onal
use
onl
y.
PILT ET AL.: POSITIVE-PARITY BANDS IN 19Si
8 (degrees)
FIG. 2. Angular distribution and best fits for the spin assignments J = 712 and J = 512 to the 4081 keV level, based on the transition to the J = 312 1273 keV level. The fit for J = 712 assumes pure quadrupole radiation.
1970) is in agreement with the 712 spin assign- ment. No direct measurement of the parity of this state has been made; however, a measure- ment of the lifetime of the state by Wozniak et al. (1969) suggests positive parity.
An a-particle bombarding energy of 5.54 MeV was used to populate this state in the 2 6 ~ g ( a , n),'si reaction, corresponding to approximately 800 keV above threshold. The y-ray angular dis- tribution of the 2808 keV y ray yielded the values a, = 0.37 f 0.02 and a, = -0.1 3 + 0.03. The nonzero value of a, immediately eliminates J = 312 from consideration for the spin of the state. J = 912 can be eliminated because of the decay to the J = 312 level, thus limiting the spin to 512 or 712. Best fits of the angular distribution with these two spin hypotheses yielded for J = 712 and pure E2 multipolarity a value x2 = 1.3 and for J = 512 a value X 2 = 6.1 at 6 = 1 .O. The latter X2 is considerably higher than the 0.1% confidence limit, thus confirming the spin assignment of 712. Figure 2 shows the
angular distribution and the best fits for spins 712 and 512.
Since the 2808 keV y ray is assumed to be pure quadrupole, the formula for polarization takes on a particularly simple form, namely
+ for no parity change - for parity change
(Poletti and Warburton 1967). Substitution of the above values of a, and a, yields polarization values of +(0.72 1 0.06), negative for a parity change and positive for no parity change. Experimentally, the measured polarization (as- suming a sensitivity R of 0.065 f 0.015) was 0.60 + 0.25. Thus there is no parity change in the transition and the parity of the 4081 keV level is established as positive, confirming the sug- gestion of Wozniak et al. (1969).
With the spin and parity of the 4081 keV level
Can
. J. P
hys.
Dow
nloa
ded
from
ww
w.n
rcre
sear
chpr
ess.
com
by
UN
IV W
IND
SOR
on
11/1
4/14
For
pers
onal
use
onl
y.
CANADIAN JOURNAL O F PHYSICS. VOL. 49, 1971
the angular distribution. The inclusion of the polarization data does not alter the general appearance of the curve, but the limits on the multipole mixing ratio can be slightly reduced. The deduced value is F = -(0.10?::::), using the 1% confidence limit of x2 for the assignment of errors. This is in reasonable agreement with the value F = -(0.05 + 0.02) reported by Fer- guson et al. (1967).
4.2 The 4742 ke V Level This level was observed to decay only to the
spin 512 state a t 2028 keV. The corresponding 2714 keV y ray was highly anisotropic (a , = 0.44 f 0 . 0 2 , ~ ~ = -0.18 +0.03).The X 2 anal- ysis of the angular distribution data alone yielded fits below the 0.1% confidence limit only for J = 912 and quadrupole radiation, and for J = 512, with F = -(1.4 + 0.30). For spin 712, the minimum of x2 was 19.8, and thus could be readily excluded (Fig. 4).
The measured polarization of the 2714 keV y ray was +0.40 f 0.27. For a pure quadrupole transition we may use [4] and the above values
-90 -60 -30 0 30 60 90 of the a, and a4 coefficients to obtain P = f (0.77 f 0.05), positive for E2 radiation and
arc tan 6 negative for M2. The measured value of the FIG. 3. x Z US. arctan 6 plot for the transition from the is in satisfactory agreement with the
4081 keV to the 2028 keV state. The analysis assumes predicted value and requires positive parity for J = 712 for the 4081 keV state, determined from the 2808 keV transition. A close inspection of the x2 curve the 4742 keV level. near 6 = 0 shows that the minimum in x 2 falls at For spin 512, the predicted polarization for the 6 = -0.10. known values of a, and a, and-the range of mixing thus determined, the angular distribution and ratios allowed by the angular distribution data polarization of the second y branch from this may be calculated using the formulas given in state, namely the 2053 keV y ray to the J" = 512' Poletti and Warburton (1967). These authors 2028 keV level was analyzed to determine the show that for a mixed quadrupole-dipole transi- multipole mixing ratio of the transition. Figure 3 tion between states of spin J , and J, the polariza- shows the x2 U S . arctan 6 plot for the analysis of tion measured a t 90" is given by
~ 5 1
where
C61
3(a, + b,) + 5/4a4 P(90) = * 2 - a , + 3/4aa
b - 8a26R2(12 J , J,) - 3[R2(11 J 1 J2 ) + 2SR2(12 J , J,) + F2~, (22 J , J,)]
If the denominator of [6] vanishes, however, all equal, the polarization is nonzero and depen- one can show a, = 0 ; the resulting indeterminate dent on the substate populations. This occurs form is then better expressed as only in very special circumstances, however; in
C71 b2 = 813 C P(MI>PZ( J1M1>R2(12 J I J z ) most cases of interest, use of [6] is perfectly M I acceptable.
6 - The R, coefficients have been tabulated by 1 + ti2 Rose and Brink (1967). Substitution ofthe known
implying that if a, = 0 and the P(M)'s are not parameters into [5] gives
Can
. J. P
hys.
Dow
nloa
ded
from
ww
w.n
rcre
sear
chpr
ess.
com
by
UN
IV W
IND
SOR
on
11/1
4/14
For
pers
onal
use
onl
y.
PILT ET AL.: POSITIVE-PARITY BANDS IN '9Si
a r c t a n 6
FIG. 4. x2 US. arctan 6 plots for the transition from the 4742 keV to the 2028 keV (J = 512) state. Only spin assign- ments J = 912 and J = 512 are not excluded at the0.1% confidence limit; however, as discussed in the text, the linear polarization of this y ray is not compatible with a spin of 512.
positive for a parity change and negative for no parity change. Neither of the above values is in very good agreement with the experimental value of P = 0.40 + 0.27; however, if the spin 512 assignment is correct, its parity must be negative and the transition to the 2028 keV state must be M2/E1. The mixing ratio solution of 6 = -(1.4 f 0.3), however, renders this highly un- likely as in conjunction with the lifetime measure- ment of Fisher et al. (1970) of (0.45 f 0.15) x 10-l3 s for the 4742 keV level, an M2 strength of 40 + 15 Weisskopf units (W.U.) would be required.
We thus conclude that the spin and parity of the 4742 keV level is 912' with 512- an extremely remote possibility. Main et al. (1970) have recently measured the 29Si(p, p'y) angular cor- relation and obtained J = 912 for the 4742 keV level, in agreement with our results.
4.3 The 5283 ke V Level The primary decay (-90%) of this state is to
the J" = 512' 2028 keV level, with a weak branch to the 1273 keV level. The angular distribution of the 3255 keV y ray is anisotropic (Table 1) and the x2 analysis (Fig. 5) is compatible with either spin 712 or 312. Even incorporating the measured
values of the y-ray polarization ( P = 0.20 f 0.25), one cannot distinguish between the two possi- bilities. Furthermore, one cannot even make an unambiguous parity assignment to this state, both negative and positive parities being allowed for either spin assignment. However, considerations based on the measured lifetime of this state (<0.1 x 10-l3 s) by Fisher et al. (1970) and on the allowed ranges of the multipole mixing ratio from the angular distribution measurements allow one to make arguments based on partial radiative widths. Table 2 summarizes the experi- mental information on the 5283 keV level and the partial radiative widths for each spin and parity assignment. It is clear that for all allowed solutions, the M2 strengths are so large as to render the corresponding negative parity assign- ments highly unlikely. Certainly for spin 312, negative parity can be rejected on this basis; for spin 712 and the smaller value of 6, the M2 strength of >24 W.U. is much larger than com- parable strengths in this region of the sd shell (Skorka et al. 1966).
Thus one can be reasonably confident in limiting the spin and parity of the 5283 keV state to 712' or 312' on the basis of these arguments.
4.4 Summary of Results A summary of the present results incorporating
the energies, spins, and parities of those levels
Can
. J. P
hys.
Dow
nloa
ded
from
ww
w.n
rcre
sear
chpr
ess.
com
by
UN
IV W
IND
SOR
on
11/1
4/14
For
pers
onal
use
onl
y.
CANADIAN JOURNAL O F PHYSICS. VOL. 49, 1971
1 ' " " " I
0 (degrees) arc tan 5 FIG. 5. Angular distribution and xZ us. arctan 6 plots for the 3255 keV y ray deexciting the 5283 keV level in ZgSi.
Both J = 312 and J = 712 give equally good fits to the data. The positive-parity assignment to this state is discussed in the text.
TABLE 2. Allowed ranges of the multipole mixing ratio 6 for the 3255 keV radiation and the hypotheses J = 712 and J = 312 for the 5283 keV level in 29Si. The corresponding radiative widths for the possible spin-
parity combinations are listed in Weisskopf units assuming a lifetime < 0.1 x 10-l3 s
Calculated strengths in W.U. Spin Allowed values
assumption of 6 lM12 (El) ]MI2 (MI) IM12 (E2) lMI2 (M2)
in 29Si and the y-ray branchings, energies, and multipolarities can be found in Table 3.
5. Discussion
5.1 General The Nilsson model as applied to 29Si (Bromley
et al. 1957; Hirko 1969) considers the low-lying levels as members of bands based on the K = 112' [211] and K = 312' [202] orbitals with oblate deformation. The 312' and 512' levels at 2426 and 2028 keV, respectively, are assigned to the decoupled ground state K = 112' band, and the 312' and 512' levels at 1273 keV and 3069 keV to the K = 312' band. Since the K = 112' band has a decoupling parameter a w - 1.25, one would expect the 912' member of this band to lie below the 712' state. The 912' state at
4742 keV, which decays'entirely to the 512' level at 2028 keV, is a natural candidate as the J = 912 member of the ground state band. The state at 5283 keV, which also decays primarily to the 2028 keV level, and which we have shown to be either J" = 712' or 3/2', may be the 712' member of this band, as its energy and decay are approximately what one would expect for such a state. The 4081 keV J" = 712' state presumably is associated with the K = 312' band decaying by quadrupole radiation to the J" = 312' band head at 1273 keV.
Additional support for these assignments is given by the existence of a J = 712 level at 3623 keV, which has been conclusively shown to have negative parity (Spear et al. 1970). As pointed out by Bromley et al. (1957) this is
Can
. J. P
hys.
Dow
nloa
ded
from
ww
w.n
rcre
sear
chpr
ess.
com
by
UN
IV W
IND
SOR
on
11/1
4/14
For
pers
onal
use
onl
y.
PILT ET AL.: POSITIVE-PARITY BANDS IN 'psi 1271
TABLE 3. Summary of the present investigation of some states in ZgSi. Excitation energies and spins and parities of the states are given, together with y-branching and y-mixing ratios
Branch E I ~ I ~ I ~ I Er1n.1 Ey ( %) JI Jr 6
5283 1273 4010 10: 5 7j2+ 3j2+ ~2 5283 1273 4010 1Ok 5 3/2+ 3/2+ Undetermined
consistent with the Nilsson model predictions 300 keV were used for all three bands in the only if 29Si is assumed to have oblate deforma- calculation. Figure 6 shows the experimental tion. level scheme as deduced from this experiment and
5.2 Coriolis Mixing Calculatior~ Inspection of the level scheme indicates that
the energies of levels of neither band follow the expected spacing for pure rotational excitation, indicating that if the Nilsson model is applicable to 29Si, coriolis mixing of the bands must be invoked in addition to decoupling of the K = 112 band in order to explain the level scheme. Such a calculation has been carried out, including the above-mentioned K" = 112' and 312' bands, as well as the K" = 112' [200] band which the Nilsson model predicts should be important for oblate deformation. Although there is little detailed experimental information concerning this excited K = 112 band one can tentatively identify the level at 4.838 MeV as the band head. This assignment is based on the experiment of Betigeri et al. (1966), who assigned J = 112' to this state on the basis of I = 0 transfer in the 28Si(d, P ) ~ ' S ~ reaction.
The calculation of the un~er turbed Nilsson wave function was carried out using a modified version of a program due originally to Chi (1969). Well parameters of K = 0.06 and p = 0.0 were used for the single neutron orbitals. These values were chosen to reproduce approximately the de- coupling of the K = 112' band and the position of the K = 312' band head and are consistent with values previously used (see e.g. Hirko 1969). The coriolis coupling calculation of the rotational bands was then applied to produce perturbed energies and wave functions of the K-mixed states. The same values for the deformation 6 = -0.08 and the rotational parameter, h2/21 =
previously existing information on 29Si and the predicted levels from the coriolis coupling calculation.
The agreement between the experimental ener- gies and the predictions are satisfactory, espe- cially for levels below 5 MeV. The 712' and 912' members of the ground state band are predicted to lie considerably higher than is observed; how- ever, considering the small number of free parameters used, we feel that the calculation agrees sufficiently well with experiment to lend support to the model.
It is interesting to note that the perturbed wave functions generated by the coriolis coupling indicate that there is rather little mixing between the ground state K = 112' and the K = 312' bands; the latter band, however, is strongly mixed with the K = 112' [200] band with a band head energy of -4 MeV. This is consistent with the fact that the latter two mixed bands both originate from the dSl2 shell model state.
5.3 Electromagnetic Transition Rates On the basis of the Nilsson model it is expected
that electric quadrupole rates for in-band y transitions would be enhanced over the single- particle Weisskopf estimates. Systematics of the sd shell (see, for example, Wilkinson 1962) indicate that for in-band E2 transitions the enhancement is of the order of 20 W.U. Out-of- band transitions, on the other hand, are expected to have E2 strengths of 11 W.U. These con- siderations, of course, apply only to pure rota- tional bands. The presence of band mixing will alter these characteristics, and, as pointed out by
Can
. J. P
hys.
Dow
nloa
ded
from
ww
w.n
rcre
sear
chpr
ess.
com
by
UN
IV W
IND
SOR
on
11/1
4/14
For
pers
onal
use
onl
y.
CANADIAN JOURNAL OF PHYSICS. VOL. 49, 1971
CORlOLlS MIXING C A L C U L A T I O N
FOR POSITIVE PARITY LEVELS IN 2 9 ~ i
= - 1 . 3 5 8 = - 0 . 0 8 h2/21 =300 kev
i 0 1/2+ - - - - - - - - - 1/2 + v2 + (211)
EXPERIMENTAL CALCULATED
29 Si
FIG. 6. Comparison of the positive-parity levels of "Si with a coriolis mixing calculation. The Nilsson model parameters used are shown; the same set of parameters were used for both the 1/2+ [211] and 3/2+ [202] orbitals. [Nn3A] are the asymptotic quantum numbers described by Nilsson. Dotted lines connecting the states indicate tentative identifications of observed and calculated levels. The observed state at 5283 keV is tentatively identified as 7/2+ 1/2+ [211] although as discussed in the text, J = 3/2+ cannot be excluded.
Malik and Scholtz (1966), a small K admixture may affect transition rates considerably. Never- theless, by comparing the in-band and out-of- band E2 strengths for the K = 1/2+ and K = 312' levels in "Si, a qualitative estimate of the importance of mixing may be obtained. Figure 7 shows the E2 transition strengths (in Weisskopf units) for a number of transitions in "Si. The experimental data (together with the appropriate reference) used in this calculation of E2 strengths are given in Table 4. It is noticed that with two exceptions, one minor, in-band E2 transition rates are at least afactorof 10strongerthan out-of-band rates. The most clearcut example is the 1273 keV y ray from the first excited state (Kn = 312') to
the ground state (K" = 1/2+) with IMI2 (E2) -- 6 W.U. The second exception involves the 5283 keV state. If one assumes that this state is indeed 7/2+ and is a member of the ground state band, and uses 6 = 0.21 for the 3255 keV transition which is favored by the xZ analysis, one finds that the out-of-band transition is approximately as fast as the in-band transition. The other value of the mixing ratio (6 = 1146 + 0.27) yields values of I MI2 (E2) which are -30 times as large for the in-band than for the out-of-band transition; however, this value of 6 is not favored by the x2 analysis. These discrepancies are at variance with the expectations of the coriolis coupling calculation which indicates that the
Can
. J. P
hys.
Dow
nloa
ded
from
ww
w.n
rcre
sear
chpr
ess.
com
by
UN
IV W
IND
SOR
on
11/1
4/14
For
pers
onal
use
onl
y.
PILT ET AL.: POSITIVEPARITY BANDS IN 19Si
E2 TRANSITION STRENGTHS IN 2 9 ~ i (W. u.)
FIG. 7. Electric quadrupole transition strengths in 29Si. The source of the lifetimes, branching ratios, and mixing ratios is given in Table 4. The notation for the decay of the 5283 keV state reflects the fact that only a lower limit can be given to the transition strengths on the basis of the measured lifetime of that state, but that the ratio of transition strengths for the 4010 and 3255 keV levels is determined from the known branching and mixing ratios.
TABLE 4. Calculated E2 transition strengths in 29Si
Transition E7
(keV) % Lifetime
Branch ( x 10-l3 S) IM(Z(W.u.)(E2)
- . . -0.2Sb -0.04'
0 0.10f 0.02'
0 0
0.21 f 0 . IS' or
1.46+0.27 'Endt and van der Leun (1967). bBecker et al. (1967). CLitherland and McCallum (1960). dMain et 01. (1970). eFerguson et 01.11967). fpreient work. '
#Fisher er 01. (1970). *Barker and Segel (1968).
Can
. J. P
hys.
Dow
nloa
ded
from
ww
w.n
rcre
sear
chpr
ess.
com
by
UN
IV W
IND
SOR
on
11/1
4/14
For
pers
onal
use
onl
y.
1274 CANADIAN JOURNAL O F PHYSICS. VOL. 49. 1971
lowest K = 112 and K = 312 bands are only slightly mixed; however, quantitative estimates of the corresponding transition strengths are required before one can make any definite state- ments concerning these discrepancies. Further Nilsson model calculations including electro- magnetic transition strengths have been initiated and it is hoped that they will indicate more pre- cisely the degree of success of the Nilsson model in explaining 29Si.
6. Summary and Conclusions
A combination of linear polarization and angular distribution measurements has estab- lished spins and parities of the following states in 29Si: 4081 keV, 712' ; 4742 keV, 912' ; 5283 keV, 712' or 312' These levels are considered in the Nilsson picture and tentatively assigned as higher-spin members of rotational bands based on the Kn = 112' 12111 and K n = 312' [202] orbitals. A coriolis coupling calculation including the above two orbitals as well as the Kn = 112' [200] orbital, and involving a minimum of adjustable parameters has successfully predicted the positions of several levels belonging to these bands. E2 transition strengths, calculated from previously known data on 29Si as well as the results of the present experiment, are also in general qualitative agreement with the expec- tations of the model.
Acknowledgments
We are grateful to J. E. Cairns for assistance with data reduction, to Dr. M. W. Greene and Dr. D. C. Kean for a critical reading of the manu- script and their comments, and to R. O'Neil for discussions on coriolis mixing. This work was supported in part by a grant from the National Research Council of Canada.
BARDIN, T. T., BECKER, J. A., FISHER, T. R., and JONES, A. D. W. 1970. Phys. Rev. Lett. 24, 772.
BARKER, S. I. and SEGEL, R. E. 1968. Phys. Rev. 170, 1046.
BAXTER, A. M., GILLESPIE, B. W. J., and KUEHNER, J. A. 1970. Can. J. Phys. 48, 2434.
BECKER, I. A., CHASE, L. F., and MCDONALD, R. E. 1967. Phys. Rev. 157, 967.
BETIGERI, M., BOCK, R., DUHM, H. H., MARTIN, S., and STOCK, R. 1966. Z. Naturforsch. 21a, 980.
BROMLEY, D. A., GOVE, H. E., and LITHERLAND, A. E. 1957. Can. J. Phys. 35, 1057.
CASTEL, B., STEWART, K. W. C., and HARVEY, M. 1970. Can. J. Phys. 48, 1490.
CHI, B. E. 1969. State University of New York at Albany. Unpublished.
ENDT, P. M. and VAN DER LEUN, C. 1967. Nucl. Phys. A, 105, 1.
ERICSON, T. 1963. Ann. Phys. (New York), 23, 390. EWAN, G. T., ANDERSSON, G. I., BARTHOLOMEW, G. A.,
and LITHERLAND, A. E. 1969. Phys. Lett. 29B, 325. FERGUSON, A. J., SMULDERS, P. J. M., ALEXANDER, T. K.,
BROUDE, C., KUEHNER, I. A., LITHERLAND, A. E., and OLLERHEAD, R. W. 1967. Proceedings of the Int. Conf. on Nuclear Structure, Tokyo, Report No. 4, 100, 145.
FISHER, T. R., BARDIN, T. T., BECKER, J. A., and JONES, A. D. W. 1970. Bull. Am. Phys. Soc. 15, 600.
HAY, H. 1969. Australian National University, Canberra, Australia. Unpublished.
HIRKO, R. G. 1969. Ph.D. Thesis, Yale University, New Haven, Connecticut. Unpublished.
JONES, A. D. W., BECKER, J. A., MCDONALD, R. E., and POLETTI, A. R. 1970. Phys. Rev. C, 1, 1000.
LAM, S. T. 1970. University of Toronto, Toronto, Ontario. Unpublished.
LITHERLAND, A. E. and MCCALLUM, G. J. 1960. Can. J. Phys. 38, 927.
LITHERLAND, A. E., EWAN, G. T., and LAM, S. T., 1970. Can. J. Phys. 48, 2320.
MAIN, I. et a/. 1970. University of Liverpool, Liverpool, England. Unpublished.
MALIK, F. B. and SCHOLTZ, W. 1966. Phys. Rev. 150,919. MEYER-~CH~~TZME~STER, L., GEMMELL, D. S., HOLLAND,
R. E., KUCHNIR, F. T., OHNUMA, H., and PUTTA- SWAMY, N. G. 1969. Phys. Rev. 187, 1210.
POLETTI, A. R. and WARBURTON, E. K. 1967. Phys. Rev. 164, 1479.
ROSE, H. J. and BRINK, D. M. 1967. Rev. Mod. Phys. 39, 306.
SKORKA, S. J., HERTEL, J. and RETZ-SCHMIDT, T. W. 1966. Nuclear Data A, 2, 347.
SPEAR, R. H., CAIRNS, I. E., ELLIOTT, R. V., KUEHNER, J. A., and PILT, A. A. 1971. Can. J. Phys. 49, 355.
TWIN, P. J., OLSEN, W. C., and SHEPPARD, D. M. 1970. Nucl. Phys. A, 143, 481.
WILKINSON, D. H. 1962. In Nuclear spectroscopy, Vol. B, edited by F. Ajzenberg-Selove, (Academic Press, New York), p. 852ff.
WOZNIAK, M. J., JR., HERSHBERGER, R. L. and DONAHUE, D. J. 1969. Phys. Rev. 181, 1580.
Can
. J. P
hys.
Dow
nloa
ded
from
ww
w.n
rcre
sear
chpr
ess.
com
by
UN
IV W
IND
SOR
on
11/1
4/14
For
pers
onal
use
onl
y.