Spectroscopic information on 24Mg and 28Si from proton capture

Nuclear Physics North-Holland

A510 (1990) 209-243

SPECTROSCOPIC INFORMATION ON 24Mg AND “Si FROM PROTON CAPTURE P.M.

ENDT,

C. ALDERLIESTEN,

Fysisch Laboratorium,

F. ZIJDERHAND,

Utrecht University,

A.A. WOLTERS

and

A.G.M.

VAN

HEES

P.O. Box 80.000, 3508 TA Utrecht, The Netherlands

Received 7 August 1989 (Revised 26 September 1989) Abstract: Gamma-ray spectra with good statistics have been measured at three a3Na(p, y)“‘Mg and five 27Al(p, y)*sSi resonances. The E, = 9.30 MeV level of 24Mg is proved to be a triplet, and those at 9.53 and 10.66 MeV of 24Mg and at 10.67 MeV of “Si are found to be doublets. Substantial improvements over previous work are obtained in the y-ray branchings of the resonances and bound states, in excitation energies, and in lifetimes of %i levels (from observed Doppler shifts). The new information has led to new J”; T assignments (or restrictions) for 16 levels of 24Mg and 16 of %i. A shell-model calculation has helped to clarify the level schemes of both nuclei, in particular with regard to the T = 1 states. New information has also been obtained on levels close above the a-particle binding energy, which are important in nucleosynthesis.

E

NUCLEAR REACTION Z3Na(p, y), E = 1020, 1318, 1417 keV; measured u(E, E,). 24Mg deduced levels, y-branchings, J, rr, T. “Al(p, y), E = 655,760,767,992,1317 keV; measured cr(E, E,). ‘*Si deduced levels, y-branchings, T,,2, J, m, T Ge detectors with, without Compton suppression.

1. Introduction The intensity calibration of Ge detectors can be extended to y-ray energies above those provided by radioactive sources with the help of -y-rays from (p, y) reactions. Most suitable for this purpose are strong (p, y) resonances which decay through a single y-ray cascade, with one cascade branch in the energy range covered by radioactive sources. This ideal situation is rarely reproduced in nature, and consequently the decay spectra of such resonances have to be investigated in detail to determine to what extent the intensities of primary and secondary in the main cascade are equal. The experimental work to be described below originated specifically from the need for high-energy intensity calibrations, and the suitability of cascades selected for this purpose will be discussed elsewhere ‘). The measured spectra, however, partly obtained with a Compton-suppression Ge spectrometer (CSS), proved to be of such high quality, both as to statistics and to resolution, that they also provided a wealth of new spectroscopic information on 24Mg and *‘Si. Four previously unobserved levels were found and many new y-decay branches, energies were determined with much greater precision, lifetimes in “Si 0375-9474/90/$03.50 (North-Holland)

@ Elsevier

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Publishers

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P.M. Endt et al. / Spectroscopic information

210

were measured determined

from observed

(or restricted)

Doppler

for many

shifts

and,

finally,

J”;T

values

could

be

levels.

2. Experiment Apparatus

(accelerator,

target

holder,

CSS),

experimental

procedure,

and data

acquisition and analysis were essentially as described in refs. 2,3). Proton currents of 75-180 p.A were produced by the Utrecht 3 MV Van de Graaff generator. Targets were Na,WO, or Al (thickness 5-30 Fg/cm2) evaporated onto 0.3 mm thick watercooled Na-free Ta backings. Hyperpure n-type Ge detectors (-y-X) of 90 or 95 cm3 active volume and a 126 cm3 Ge(Li) detector have been used in a Compton suppression shield and all three of them, in addition to a 100 cm3 Ge(Li) detector, have also been used unshielded. In table 1 the experimental conditions are listed for measurements of (p, y) spectra and y-ray angular distributions at different resonances. In particular at the strong E, = 992 keV 27Al(p, -y) resonance exceptionally good statistics were obtained. In the corresponding CSS spectrum the E, = 1.78 MeV transition in **Si (first excited state to ground state) contains 1.9 x lo7 pulses. Spectra of (on the average) 600 PAh taken a few keV below and mostly also a few keV above every resonance (except for the E, = 760 keV 27Al(p, y) resonance, see below), served to subtract possible contributions

of neighbouring

resonances.

TABLE Experimental

1020 1318 1417

2200 2500 3200

655 760 767 767 992 992 1317 1317

440 600 1900 500 7000 320 2400 500

‘)

‘) ‘) ‘)

the spectrum

at E, = 760 keV

1

for measurements Detector

It “) I@hl

Reaction

*‘Al(p, y)28Si

conditions

Actually

of (p, y) spectra

A ‘)

Detector

B ‘)

type

angle [deg]

type

angle [deg]

y-x2 css 126 cm3 CSS y-x2 css

55 55 55

126 cm3 U 100 cm3 U 126 cm3 U

-90

y-x2 u y-x2 css y-Xl css y-x2 u y-x2 css y-x2 u y-Xl css y-x2 u

AD 55 55 AD 55 AD 55 AD

y-Xl css 126 cm3 U

AD -90

100 cm3 U y-Xl css 126 cm3 U

-55 AD -90

-90 -90

“) Proton current (in pA) times measuring time (in hours). ‘) The symbols y-Xl and y-X2 denote the 90 cm3 and the 95 cm3 Ge detector, respectively, while U and AD stand for unshielded detector and angular distribution measurement, respectively. For the latter measurements spectra were taken at 0 = 0”, 30”, 45”, 60”, and 90’. ‘) Total proton charge per angle.

P.M.

had been taken as something

as “a few keV below distribution

correct

the intensities

equally

well to determine

discussion

211

et al. / Spectroscopic i~~o~ation

the E, = 767 keV resonance”,

and thus came

of a by-product.

The angular

analysing

En&

measurements

at @=55”

the measured of contaminant

for angular

lifetimes spectra

listed in table

from

distribution

Doppler

are explained

1 had been performed effects,

shifts.

in detail

to

but they served

The methods

used

for

in ref. 3). This includes

a

lines.

3. The Z3Na(p, Y)‘~M~ reaction The y-ray branchings of the three resonances investigated here are listed in table 2. Previous 23Na(p, y) work by Meyer et al. “) and Boydell and Sargood ‘) had yielded a total number of 21 and 12 primaries, respectively, to be compared to the 67 primaries listed in table 2. The gain in sensitivity of the present work for the detection of weak lines, in particular at low y-ray energy, mainly results from the Compton suppression, but also from better statistics and better resolution. In table 3 the observed y-ray branchings of secondafy states of 24Mg are given as compared to those known from previous work. About 35 of the branchings listed were previously unobserved, many others have obtained smaller errors. For some weakly excited secondary states not listed in table 3 the measured branchings were either in agreement with or had larger errors than those given in ref. “). Excitation energies of 24Mg levels have been obtained from internal calibrations based on the accurate energies given in ref. ‘) for E, = 1.37 and 4.12 MeV, and in ref. “) for E, = 4.24,5.24,6.01,7.35,7.62 and 9.301 MeV (see table 4). Most information has been derived from the spectra at @= 90” (where lines are in first order not Doppler shifted), but for some levels the 8 = 55” CSS spectra have also been used for primary y-rays which were taken to be fully Doppler shifted; see also sect. 4. Recoil corrections

have been applied

in the conversion

from E, to AE,.

Most useful

has been the E, = 1417 keV J” = 4+ resonance because in its decay the largest number of calibration levels (also with relatively high spin) is excited. Much harder were energy determinations at the Ep = 1020 keV resonance because, to start off with, the calibration curve at 8 = 90” could only be constructed up to E, = 3.87 MeV, corresponding transition, at other resonances

to the 5.24+ 1.37 MeV transition. The 4.24-+ 0 MeV a good calibration point, could not be used because

it almost coincides with the r+ 8.438 MeV primary. Strong cascades starting at the resonance, which could have been used to determine the resonance excitation energy E, if all components have E, < 3.87 MeV, are absent. It turned out, however, that both E, and the excitation energies of the 7.75 and 8.86 MeV levels could be determined with about 0.2 keV precision by means of a smooth extension of the calibration curve, constructed such that it contains the rj4.24, 7.75 and 8.86 MeV primaries and the 7.75 + 1.37, 8.86 + 1.37 and 8.86 + 4.24 MeV secondaries.

212

P.M. Endt et al. / Spectroscopic

information

TABLE 2 Gamma-ray branchings (in %) of Z3Na(p, y)24Mg E,= 1020, 1318 and 1417 keV resonances (E, in keV) “)

J;; Tr 0+

2+ 4+ 2+ 3+ 4+ 0+ 2+ 1;; (4_, 5+) 312+ 22+ 12+ (3&f)(o+-2) (2,3)+ (233); 0 1+;0+1 +. :-: :, (1,2)+; 1 o+; 0 3-; 0 +. its;; (3,4)+ o+;o 1+; 1 2+;0 3+ 2+;0 (l-3) 2+;0+1 4+; 0 (2+-4+) 2+;0 2+;0 (3-5)

E Xl

0

1369 4123 4238 5235 6010 6433 7349 7555 7616 7748 7812 8358 8438 8655 8865 9004 9146 9284 9300 9301 9305 9458 9533 9828 9968 10028 10059 10111 10334 10361 10581 10660A 106608 10680 10712 10731 10821 10917 11187 11208 11217 11330 11453 11988 12128

J:;Ti: Exi : E,:

2-; 1 12 670 1020

1+; 1 12 955 1318

0.25 3 10.3 4

8.2 3 85.6 4

59.6 8 0.06 2

0.039 9 1.51 6 0.028 10 4.10 13

4+;0+1 13 050 1417

0.08 1 90.6 2

0.96 3 1.43 5 1.66 5 1.00 3 0.14 5 0.012 4 0.012 2 0.181 7

1.40 5 3.0 3 0.28 2 14.3 5 0.40 3 0.27 2 0.67 3

0.055 4 0.168 8 0.269 I1 0.026 2 0.56 2 0.126 5 0.08 3 0.32 3 0.69 2 2.28 7

1.21 5 0.61 3 0.170 12

0.76 2 0.025 3 0.47 2

0.15 2 0.166 12 0.022 10

0.134 6 0.105 5 1.22 4 2.07 6

0.099 10 0.276 11 0.252 13 0.48 2 0.041 8 0.065 7 0.113 10 0.12 2

0.018 3 0.014 4 0.047 5

0.288 11 0.019 6 0.102 11 0.212 11

0.052 12

“) For E, and J”;T, see tables 4 and 5, respectively, and ref. 6).

0.036 4

P.M. Endt et al. / Spectroscopic

The above

213

information

calibration curve at the E, = 1318 keV resonance E, =4.24 MeV by using the energies of several

1020 keV. The results, as compared

could be extended levels determined at

E, =

4. Although represents

the precision on the average

of the values

to the E, values from previous is not as good as obtained a substantial

listed in the 1978 evaluation

improvement

work, are shown in table

for *%i (see sect. 4), it still of a factor 7 over the precision

“). The present

values might be systemati-

cally somewhat higher than those from ref. “) but for most levels the difference stays well within the combined error. Finally, we list in table 5 the J”;T assignments and restrictions to which the present work has contributed, for altogether 16 states. Some levels are also included which are not listed in table 2 as secondary states, but which are important for the discussion of the multiplets given below. The J”;T restrictions from y-decay and y-feedings are based on the recommended upper limits (RUL) given in ref. ‘). The transition strengths are based on the lifetimes given in refs. 6,‘o) and, for the resonances, on the resonance strengths from ref. I’). One might be inclined to accept also T = 0 admixtures in the wave functions of the E, = 12 670 and 12 955 keV T = 1 states, because in ref. “) it is claimed that these levels also (very weakly) resonate in the yield of the E, = 1.63 MeV y-ray resulting as observed with a NaI detector. We are from the 23Na(p, cu,y)*‘Ne reaction, convinced, however, that this is not justified because ref. “) fails to prove that the Compton contributions from the corresponding strong (p, y) resonances in the channel set around E, = 1.63 MeV are properly subtracted. Analogous erroneous background subtraction has been found ‘) for the 25Mg(p, p’y)25Mg yield curve of ref. 45). Three levels are excited (see table 2) in the neighbourhood of E, = 9.30 MeV. The energies are 9299.8 3, 9300.95 15 and 9305.4 3 keV. The 9300 keV level has been observed 12) in the “Ne(a, y)24Mg reaction with an energy of 9300 2 keV and with J” restricted to J” = (3,4)-. A J” = 4+ assignment to the 9301 keV level has already been given in ref. 13). The decay of the E, = 1318 keV 23Na(p, y) resonance to the E, = 9305 keV level has also been reported in ref. 14), with the energy given as E, = 9306 5 keV. In the 1978 review “) this energy was erroneously ascribed to the 9300 keV (3,4)- level. We conclude that it is only through the present work that the existence of a triplet at E, = 9.30 MeV has definitely been established. The 1978 review 6> lists 24Mg levels at E, = 9521 3 and 9528 2 keV, the latter with J” = 6+. We are not convinced that the former level does exist. It has only been observed in the 24Mg(p, p’) reaction 15) as an inconspicious asymmetry in the high-energy slope of the strong proton peak corresponding to the 9528 keV level. The latter level is well established 16). The level found in the present work at E, = 9532.7 2 keV with J = (2,3) should be considered as previously unobserved. The existence of a doublet at E, = 10.58 MeV has already been reported in ref. ‘). The level which we observe at E, = 10 581.26 13 keV should correspond to the level

214

P.M. Endt et al. / Spectroscopic information

P.M. Endt et al. 1 Spectroscopic information

a

m-

215

216

P.M. Endt et al. / Spectroscopic

information

TABLE 4 Excitation energies (in keV) of z4Mg levels from present and previous work Present results E, = 1020

1318

6432.5 2 7555.3 3 7747.7 2 8358.1 8438.2 8654.9 8864.7 9003.5 9146.2 9284.4

3 2 4 2 3 3 3

8438.6 3 8864.2 3 9003.4 3

9305.4 3

9532.7 2 9828.6 2 9967.8 3

1417

9828.0 3 10027.90 17

10333.6 2 10360.7 3 10581.26 13 10659.8 2 10660.17 17 10679.7 3 2 2 3 3 11216.69 18 11452.8 4 11988.0 3 12669.9 2 12954.9 2 13050.22 14 “) b, ‘) ‘)

average

[1368.675 61”) [4122.875 151”) [4238.36 61”) r5235.20 81”) [6010.32 91”) 6432.5 2 [7349.05 41”) 7555.3 3 [7616.47 91”) 7747.7 2 7812.2 3 7812.2 3 8358.1 3 8438.4 2 8654.9 4 8864.5 2 9003.5 2 9146.2 3 9284.4 3 9299.8 3 9299.8 3 [9300.95 151”) 9305.4 3 9457.80 12 9457.80 12

10059.1 4 10110.9 4

10712.2 10731.1 10917.2 11187.3

Previous work

9532.7 2 9828.4 2 9967.8 3 10027.90 17 10059.1 4 10110.9 4 10333.6 2 10360.7 3 10581.26 13 10659.8 2 10660.17 17 I 10679.7 3 10712.2 2 10731.1 2 10917.2 3 11187.3 3 11216.69 18 11452.8 4 11988.0 3 12669.9 2 12954.9 2 13050.22 14

ref. 6,

ref. *)

1368.59 4 4122.82 7 4238.4 2 5236.1 4 6010.3 4 6432.2 5 7347.9 7 7553 2 7616.2 5 7747.2 5 7812.0 9 8357.7 6 8438 2 8653.4 7 8863.1 9 9002.1 10 9148 3 9283 2 9306 5 9298 2

other refs.

[1368.675 61 b, 1368.675 6 ‘) [4122.875 IS] b, 4122.875 15’) 4238.36 6 5235.20 8 6010.32 9 7349.05 4 7616.47 9

9300 2 d) 9300.95 15

9455.8 7 9528 2 9827 2 9966 2 10026 2 10059.0 IO 10112 3 10328 3 10357 2 10580 ‘) 10660.3 IO 10680 3 10711.7 10731.4 10922 3 11186 3 11217 3 11455 5 11985.9 12668.2 12953.5 13048.1

8 15

8 7 ‘) 6 ‘) 6 ‘)

Used as calibration energies in the present work. Used as calibration energies in ref. ‘). Ref. ‘). d, Ref. I’). “) Ref. 5). As calculated from E, in ref. “) and Q(p, y) = 11690.8 6 keV from ref. 26).

P.M. Endt et al. / Spectroscopic information

217

TABLE 5 Arguments

[k%]

7812* 9300 9301 9305’ 9458* 9521 9533* 9828* 10059 10334 10576 10581* 10660** 10660a* 10731 10824* 11187* 11208 11217 11330* 11988* 12128* 12670* 12955* 13050*

for J”; T assignments

Other refs.

Ref. “)

(3+, 4-, 5+) (3-5)-

to *4Mg levels “) Present

y-decay

zo#l

1+;(1)

(l-4+) (l--3+)

;l

4+: 0

(2+-4+) (l-3) f5+

(3b!)m (o+-2)

(l-3);

0

;O

N;O’)

(3,4+) (o--4-)

;o (o+-4+)

f(4, 5)+ (o--4-)

(o+-4+)

(2+-6+)

T=l’)

2+ 21 4+(2+); 0

(O-2)

;O (3-5)

(1, a+‘)

(2, 3)+ ‘) (2, 3); 0 1+;0+1 (1,2)+; 1 33; 0 5+(3+); 0

(3, 4)+ a)

(1, a+

(4_, 5+)

T=l’) 33; OC) 5+(3+); 0 ‘*s)

(3-5)+ “) 1 N;O, #l-=)

Resulting assignment

23+ b)

24+

(2-4)’

4+ (2-4)+

y-feeding

#s-c) f3+ d)

(3,4)+

(1, a+;(1)

work

;1 T= 1, #2+

(3,4+) (l-3_) (3,4)+ 2+; 0 3+ (l-3) 2+; o+ 1 4+; 0 (2+-4+) +. (231p) 22; 1 1+; 1 4+;0+1

“) For E,, see table 4 and ref. 6). The J”; T assignments for levels marked with an asterisk result partly or altogether from the present work. For several levels with unknown lifetime the J” restrictions in the column “y-decay” are based on the rule that the decay of states at relatively high E, proceeds through Ml, El or E2 transitions. b, From 10028 + 7812 keV. ‘) Ref. r2). d, Ref. 13). ‘) Ref. 33). ‘) Ref. 24). “) Ref. s). “) Ref. s4). ‘) Ref. 35). ‘) We assume that this level does not exist (see text).

denoted as 10.58” which was also reported in ref. ‘) to be excited at the E, = 1417 keV resonance. The state listed in the review 6, at E, = 10 660.3 10 keV has also been proved to be a doublet. The two components at 10 659.8 2 and 10 660.17 17 keV, here denoted as 10660A and 10660’, decay differently (table 3). Presumably 10660B can be identified with the 10.66 MeV level which is strongly excited at the E, = 1726 keV 23Na(p, y) resonance 4*5).

P.M. Endt et al. / Spectroscopic information

218

4.

The branchings

of the five resonances

contains

134 entries,

reported

in the most exhaustive

at which

-y-ray angular

intensities

The *‘Al(p, y)**Si reaction investigated

to be compared

for the same

resonances

previous

27Al(p, y) work 17). At the four resonances have been measured (see table l), the 8 = 55”

distributions

were corrected

are listed in table 6. The table

to 55 branchings

for a possible

P,(cos

0) term in the angular

Such corrections amounted to at most a few percent. The decay of ‘*Si secondary states is presented and compared in tables 7 and 8. About 65 branches were not observed earlier. shown in fig. 1.

distribution.

with previous work A few examples are

The branching found for the 6.28 + 4.62 MeV transition (11.8 3)% is rather higher than the values given in refs. ‘7,18). The line coincides in energy with the 7.93+ 6.28 MeV transition which may cause the difference with ref. 18). The branching [ (14 5)%] given for the latter transition in ref. “) is definitely too high, whereas the authors of ref. “) seem not to have been aware of the existence of the latter transition, such that their low value [(7.5 S)%] for the 6.28 + 4.62 MeV branching is not

27Al(p,y)28Si

Ep = 655

CSS

3 = 550

keV

Ep= 1317

keV

r

8x104 t NUMBER OF COUNTS

r+10900 1316

9382-7933 1449

6

4 i

I

-

CHANNEL

NUMBER

Fig. 1. Parts of the Compton suppressed y-ray spectra at the E,= 655 and 1317 keV *‘Al(p, y)*% resonances, showing the previously unobserved r+ 10.90, 6.89+ 4.62 and 9.38 + 7.93 MeV transitions.

TABLE

6

Gamma-ray branchings (in X) of five *‘Al(p, y)?Si JF; T,:

J;; Tr

0

0+

:I 3+ 34+ 2+ 2+ 3+ 2+ 2+ 1+ 46+ 3+ 15+ 4+ 3+; 1 2+; 1 4+ 2+ 1+ 5;s 135(2-45: 3+; 1 5+ (1-3:: 1+; C&3)+; 4+; 1+; (293); 1+; 2+;

o+ 1 0 0 o+ 1 1 1 0

;: (2-4+) (2+-4+); 2+; 2+; 4+; 1+; 6+; 3-; (3-5+)

E xf

0 0 o+ 1 o+ 1 1 0 0

1779 4618 6276 6879 6888 7381 7416 7799 7933 8259 8328 8413 8544 8589 8905 8945 9165 9316 9382 9417 9479 9496 9702 9765 9796 9929 10182 10190 10209 10311 10376 10418 10514 10540 10596 10668A 106686 10725 10883 10900 10916 10944 10951 11079 11195 11265 11433 11435 11446 11509b) 11585 12174

E,,: E,:

2-; 0 12216 655 2.2 2 42.1 10 4.5 2 1.63 9

resonances (E, and E,, in keV) “)

2-;o 12318 760 1.5 2 86.6 2 0.13 3 1.32 7

4+ 12324 767

3+; 1 12541 992

0.51 4 75.0 2 3.60 11 0.83 3 1.46 5

76.4 4 4.09 12 2.15 7 0.70 2 0.294 9 0.187 6 0.297 9 8.5 3 3.96 12 0.023 8

11.9 4 11.5 4 45.8 7 0.135 8 7.5 3 0.48 2 0.47 2 5.5 2 0.187 10 0.12 2

0.95 5 1.82 10 0.05 3 6.4 2 1.60 9 1.27 7 0.49 5 3.36 13

2.09 9 29.1 9 0.06 3 0.30 5 0.07 3

4+;0+1 12854 1317

2.38 7

0.81 3

0.26 3

3.29 10

0.007 2

0.24 3 0.10 2

4.89 15

0.173 6

0.37 2 0.081 11 1.34 4

0.11 1 5.41 16 0.009 4 0.29 1 0.05 2

0.147 5 0.047 2 0.012 2 0.79 3 1.11 4

1.30 4 0.051 6 5.7 2 0.36 2 0.083 6 0.125 7

3.71 12 0.08 1

0.23 6 0.13 2 0.050 12

0.10 1 2.60 8

0.45 2 0.195 7 0.035 2

0.02 1 0.05 1 0.10 1 0.09 3 0.52 3

0.12 3 1.39 7

0.31 1 0.11 1

0.085 3 0.146 5 0.061 3 0.016 1

0.12 2 0.20 2 0.20 2 0.08 2

0.026 0.370 0.411 0.021 0.181 0.441 0.016

4 13 14 5 8 14 4

0.288 9 4.50 15

0.162 0.63 4

1.19 4 0.09 2 0.04 I 0.06 2 0.010 4

0.12 2

0.013 0.046 0.089 0.082

2 4 3 3

0.417 14 0.011 3

0.043 4

0.06 2 0.21 1

0.018 2

0.09 2

0.023 2

0.034 10

0.28 3

“) For E, and J”; T, see tables 9 and 12, respectively, and ref. 6). b, Ref. 36).

0.025 5 0.019 2

E,;

6276

6879

6888

7381

7799

7933

8328

8413

8589

8945

9316

9382

9417

9479

9765

JT;T,

3+

3-

4+

2+

3+

2+

1+

4-

3+

5+

3+; 1

2+; 1

4+

2+

3-

TABLE 7

85 2 85 5 10.8 <2

3.2 4 3.4 5

83.4 15 822 76 5 58 5 124

38.4 12 37.5 15 36.3 5

70.0 11 64 2

_r;:o+ E,,: 0

97.0 3 85 5

69 2 74.5 9 89.3 11 92.5 8 33.1 JO 26 5 2.58 12

11.8 3 7.5 5 6.9 14 2.1 4 3.0 7 1.29 8 il il C2

88.2 3 92.5 5 93.1 14 27.3 10 33 2 98.71 8 100 61.6 1.7 62.5 I5 63.4 5 65 2 70.0 10 66.2 11 5.5 2 4.5 20 3.9 4 26 5 28 4 17.1 6 22 2 88.0 4 91.4 7

<0.4 C5

2.8 2 4.0 15 4.3 2 3.2 6 58 2 642 603 0.34 6 10.4 to.2 <3 36.1 14 38 4 6.4 3

1.32 8 1.04 1.2 I 4.7 2 7.8 13 3.63

4+ 4618

2+ 1779

4.5 15

CO.2 <2

4.02 5.7 15 2.9 2 <3 <5

0.3 1

<1

0+ 4980

2.5 3

28 2 23.7 8 4.0 2 4.1 6 3.1 2 52 <2

CO.8 CO.4 6.9 2 5.42 CO.7

14 5 162

342 29.0 10 32.6 11 2.4 12

qo.2 il <1.5 Xl

Cl.5

3+ 6276

0.55 15

Cl.2

<0.6

10.2 x0.15 <0.2

80.1 6 74 2 CO.2

CO.15

CO.07

36879

10.3

0.6 2 (15 5) CO.8

1.22

CO.2 CO.4 CO.1

422 362 40 3 CO.1 x0.4 CO.2 18.7 6 23 5 Cl.2

CO.5

2+ 7381

0.3 2

<0.2

0.14 2

4+ 6888

CO.8

0.7 5 82 0.49 6

<0.2 CO.2 0.11 6

2* 7416

to.4

to.4

5.63

1.7 4 1.8 1 CO.9

0.52 8

3+ 7799

~0.6

1.5 2

2.82

0.70 10

2+ 7933

Gamma-ray branchings (in %) of secondary statea in ‘*Si (E, in keV) from present and previous work “)

unknown 15

+8259 0.54 16

-8589 0.6 2

To other levels

,’

1

i

“)

17

)

17 )

18 )

181

37

17

1s

36

17

Refs.

P.M. Endt et al. / Spectroscopic

information

222

P.M. En& et al. J’ Spectroscopic

information

TABLE 8 Decay and feeding intensities I,“) and decay branchings (in %) of the components of the 10.67 MeV doublet; it is assumed that different levels are excited at the 992 and 1317 keV resonances, denoted in the text as 10668* and 10668’, respectively. E, = 992 keV

E,=1317keV

b(r) ? 1, 10668 + 0 --f 1779 + 4618 -$ 4980 + 6276 + 6879 + 6888 -P 7381 -+ 7416 + 7799 -) 7933 + 8259 + 8544 + 8589 + 8945 -, 9316 + 9382 -+ 9417 unknown

c= r + 10668

b(r)

<45 206 25 <25

cs

45 12
5.3 I4 Cl 6.8 5 2.1 4 11.2 7 (1 1.1 3 <0.8 ~0.6 <2 CO.9 493 Cl.5 qo.4

24 3 <3

1, Cl4 158 7 190 13 16 510 17 (7 35 4 103 313 10 39 3 145 5 182 8.8 14 137 5 204 508 16 7.7 23 9.1 17

b(r) 10.6 62
co.7 1.5 3 9.0 6 <0.3 24.2 8 CO.3 1.72 0.47 14 14.8 5 1.85 14 6.9 2 0.85 9 0.42 7 6.5 2 0.95 f9 24.1 8 0.37 11 0.43 8

92

72 20 2 52

847 39 893 27

100

2109 66 2105 63

100

30 100

“) The intensity of a transition is defined as the number of pulses in the corresponding fult-energy peak divided by the detector efficiency E, the latter normalised such that E = 100 at E, = 1 MeV. b, From ref. I’).

understood. The present branching is the average of the values (11.9 4)% and (11.8 4)% obtained at the E,= 767 and 1317 keV resonances; at both resonances the 7.93 + 6.28 MeV contribution to the intensity of the 1.66 MeV peak is quite small (-0.3%). Excitation energies of *‘Si levels are listed in table 9. We see that, as compared to 24Mg (table 4), rather more and more accurate energies could be determined in *‘Si. Yet they are all based on a single calibration energy, E, = 1779.030 11 keV for *‘Si( 1) from ref. ‘*). In the unsuppressed 90” spectra the E, = 1.78 MeV line and its escape peaks provide the first three calibration points. The energy of the E,= 4.62 MeV level can be determined through the double-escape peak (at E, = 1.82 MeV) of the 4.62+ 1.78 MeV transition, which is very close to E, = 1.78 MeV. This then provides new calibration points at E, = 2.84 and 2.33 h/ieV. The energy of the E, = 6.28 MeV level is found from the E, = 1.66 MeV 6.28 + 4.62 MeV transi-

P.M. Endt et al. / Spectroscopic information

tion

(see above).

The 6.28 + 1.78 MeV transition

223

now yields

calibration

points

at

E, = 4.50, 3.99and 3.48 MeV. In this way levels can be added at ever higher E, in successive

steps, with a concomitant

of levels with well determined the primaries

to these levels

extension

energies

includes

of the calibration

line. When the set

levels in the E, = 7-9MeV region,

can be used to obtain

the resonance

energy.

Finally,

the energies of weakly excited levels in the E, = 9-12MeV region are then determined through the energies of their corresponding (low-energy) primaries. It should be noted that for relatively strongly excited levels the entries in table 9 are weighted averages of several (often many) independent determinations. Decay lines may have been suitable in addition to the primary, and escape peaks may have been used in addition to the full-energy peak. The errors assigned to the entries in the first eight columns of table 9 are purely statistical. They result from the statistical errors of the peak positions and from the quality of the calibration curves used to convert peak positions into energies. For five out of the eight spectra listed in table 9 the calibration curves are quite beautiful. They are of almost parabolic shape with a deviation from a straight line which does not exceed 0.3 keV over an energy region of about 8 MeV. The calibration curves for the other three spectra were also of almost parabolic shape but with a much larger deviation from a straight line. In addition to the statistical errors we consider three main causes of systematic errors. The error of 11 eV in the calibration energy introduces for a level E, an error which, from the calibration procedure outlined above, is then to be about equal to (AE,),,, = (E,- 1022)x 0.01 l/1779 keV. The errors in the weighted averages (column nine of table 9) are obtained by adding this calibration error in quadrature to the statistical errors. The calibration error is substantial and effects, for instance for the resonance levels, a ratio of the total adopted error over the statistical error of about a factor 2.5. Second, one has to consider the accuracy with which detectors can be positioned at 13= 90”. The estimated 0.5” deviation from the 90” position would introduce a difference in the energies of fully shifted and of unshifted lines increasing from 12ppm at E,=655 keV up to 17 ppm at E,= 1317 keV, which would also lead to considerable

errors,

somewhat

larger than

the calibration

errors

discussed

above.

For each measurement, however, detectors have been positioned anew, such that the errors in different spectra are uncorrelated. In some spectra, moreover, the contaminant lines at E, = 1.46, 2.61 and 6.13 MeV due to the radioactive decay of 40K and “‘Tl and to the 19F(p, ay)160 reaction, respectively, had sufficient intensity to serve as checks. In all cases these lines fell within the error on the calibration curves constructed as outlined above. The mutual consistency of energies determined at different resonances also strengthens our confidence in the correctness of the 90” detector positioning. The average ratio of the external over the internal statistical error of the weighted averages in table 9 amounts to 0.98, very close to the expected value of unity.

224

I? hf. Endt et al. / Spectroscopic infomation

P.M. Endt et al. / Spectroscopic information

G-3 me-

225

226

P.M. Endt et al. / Spectroscopic

Finally,

we have to consider

not only of full-energy (DE)

peaks.

reported

systematic

errors

connected

(FE) peaks, but also of single-escape

Deviation

varying

possible

information

of the FE-SE

and SE-DE

with our use

(SE) and double-escape

differences

from m,c2 have been

from a few eV [refs. ‘,19)] to a few hundred

eV [refs. 20,21)]. The

deviations depend on the type of detector and the detector geometry and on the peak fitting programme used 19), but they seem to be independent of E, [refs. “~“)]. Several

of our spectra,

especially

those

with an almost

linear

energy

calibration

curve, were good enough to allow an independent determination of the deviations in question. For the unshielded y-X detectors we find from nine FE, SE, DE triplets EFE - Es, - m,c2 = 117 20 eV, EFE - EDE- 2m,c* = 94 21 eV, and for a y-X detector in the Compton suppression mode ErE- ESE- m,c2 = 85 21 eV. We conclude that the FE-SE and FE-DE deviations are equal within the errors, and that the same applies to the FE-SE deviations measured either with or without Compton suppression. The average deviation amounts to about 100 eV, which accordingly was applied as a correction to all escape peaks in spectra from the y-X detector. For unshielded 126 cm3 Ge( Li) detector the deviations were found to be zero within the error. The final systematic error in measured excitation energies caused by the error of about 20 eV in the m,c* corrections is small compared to the two systematic errors discussed above, and thus could be neglected. We also want to discuss two minor possible sources of errors affecting our y-ray measurements. The y-ray energy measured with the CSS at 0 = 55” has to be corrected for Doppler shift, which in principle should be averaged over the finite solid angle of the detector, set-up (angular

taking into account the -y-ray angular distribution. For the present opening *7”) the point detector approximation has been used, which

overestimates the shift by 0.4% for isotropic radiation, with an additional for extreme anisotropies. In first instance, this implies effects of typically which are further reduced, to a negligible level, by the procedure of internal

*0.4% 10 eV, energy

calibration. The second-order Doppler shift has to be considered even at f3= 90”. If the present E, values were derived from (i) fully shifted reaction lines measured relative to (ii) unshifted

calibration

lines with (iii) the ground

state as the only basis, the second-

order effects would range up to 34 eV (for the 23Na(p, y)24Mg, E,= 1417 keV resonance state). Neither of the assumptions (i) or (ii) is, however, fulfilled in the calibration procedure, while assumption (iii) does not hold for 24Mg (see table 4, footnote “)). On closer inspection the error due to the second-order effect is well below 10 eV for the present excitation energies, and thus has been neglected. In table 10 the present **Si excitation energies are compared with those from previous work. The agreement with the 1978 evaluation “) and also with ref. 18) is seen to be amazingly good. For none of the levels energy differences exceed three times the combined error and systematic differences seem to be absent. It has already been mentioned that the -y-ray angular distribution measurements performed at four *‘Al(p, 7) resonances could be used for the determination of

P.M. Endt et al. / Spectroscopic TABLE Comparison

of present

and previous

Previous

Present work

1778.79 8

1779.030

4617.86

4

4617.3 3

4617.47

4979.92

8

4979.1 5

6276.20

7

6276.3 2

6878.79

8

6887.65

10

[1779.030

II] “)

energies

(in keV) of 28Si levels Previous

Present

other refs.

ref. 6,

227

10

excitation

work

information

11 b) 15 b,

work

10181.60

ref. 6, 12

10188 3 ‘) 10210.0 8

10310.92

13

10312.1 10

6878.6 3

10376.24

12

10376.0 4

6888.8 5

10418.25 22

10418.4 16

7380.59 9

7380.7 4

10514.1 3

10514.6 17

7416.26 9

7417.3 4

7415.9

7799.01 9

7798.8 4

7933.45

8258.74

10 10 8328.38 12

15

7799.16 25 “)

10668.05

13

7933.4 4

7933.5 4 b)

10668.34

11

10668.6 16

8259.4 6

8259.0 5 b,

10883.45

14

10883.8 17

15

10901.0 15

8328.3 9 8413.3 3

10900.42

IO

8543.56 20

8542.9 9

11078.52

14

8588.71

8588.9 6

11195.22

13

8413.33

10

8904.8 4

10944.7 1.5

10944.0 3 8588.7 3 b,

8903.7

7

11265.0 3

7

11432.63

8945.20

13

8944.8

9164.68

17

9163.9 6

9315.92

10

9315.9 4

9315.121

9381.55

12

9380.5 4

9381.1 4 b)

9417.17

14

9418.1

9479.49

11

9479.9 13

9496.04

15

9702.34 9764.52 9795.95

b)

111963

18

11434.3 10

11434.50 22

11434.6 15

11446.00

16

11446.2 5

11584.62

19

11585.1 4 12174.0 3 d,

13

12215.7 3 d,

9497.3 9

12318.00

13

12317.6 3 d,

12

9702.0 4

12324.36

14

12324.1 3 d,

11

9762.8 I1

12541.31

14

12540.7 3 d,

14

9794.2 I7

12854.43

14

12854.3 3 d,

“) Calibration d, As calculated

energy. from

“)

9795.8 10 b,

Ref. Is). ‘)

10945 3 ‘)

11077.8 10

12215.97

9479.1 9 b)

10668.0 3 b)

112663

12174.3 3

7

10208.8 IS b,

10597.3 10

10596.18

7b)

other refs.

10179.9 14

10189.59 20 10209.0120

6276.34 25 “)

work

Ref. 36).

E, given in ref. “) and Q(p, y) = 11584.6 3 keV from ref. 26).

DSA lifetimes. Some details about such measurements and their evaluation is given in ref. ‘). Levels for which indirect feeding from longer-lived levels exceeds 15% of the total feeding intensity were left out of consideration. Upper and lower T, limits correspond to twice the error in F(r,). The results are shown in table 11. It is seen that for some levels (e.g. for E, = 4.62 and 6.28 MeV) the differences in the F-values measured at different resonances appreciably exceed the combined statistical errors. The main origin of these discrepancies might be the rather large uncertainty in the thickness of Al target layers. We think that this source of errors is accounted for, first by the large external errors in the adopted (average) F-values, and second by adding (in quadrature) a 15% systematic error to the corresponding lifetimes, which also takes into account the errors in the F( 7,) curves.

1779 4618 4980 6276 6879 6888 7381 7799 7933 8259 8328 8413 8544 8589 8945

[k?‘]

[k%]:

0.115 13

0.955 25

0.919 14

0.29 9

0.106 5 -0.02 4 0.758 13

0.762 12

167

0.966 26 0.939 20 0.106 24 0.23 14

0.644 21 0.100 30 0.028 16

0.125 18

655

1 7 25 2 1.5

0.960 25

0.236 14 0.924 4

0.117 0.580 0.636 0.076 0.015

992

F(T,) “)

0.81 6

0.870 4 1.05 4 0.38 7

0.155 3

1317

Doppler shift attenuations (F) and corresponding lifetimes (7,)

TABLE 11

0.117 1 0.63 8 0.641 16 0.101 25 0.019 11 0.86 3 >0.92 0.243 23 0.925 6 0.939 20 0.106 24 0.115 13 0.81 6 0.935 11 0.59 4

adopted

ref. 6,

63 6 45 JO 1200 120 2600 400 50 7 82 260 45 20 JO 15 6 260 110 430 90 18 5 12 5 85 15

present b, 880 130 84 27 81 13 990 230 >3JOO 27 8 <15 250 45 142 12 4 960 220 890 160 38 14 123 96 19

~,D-Sl

of ‘*Si levels from present and previous work

100 Ioe)

J4d) 300 75d) 15 lo*)

54 13 *) 1350 400q

690 13’)

other

2 & s

2 a x B. “. 8

. 8

F B E R

.% %

“) b, “) d, g, h,

0.99 5 1.003 25

0.990 14

0.971 20 0.993 2

1.001 9

0.984 9

0.879 25

1.002 22 1.048 30 0.84 8

0.581 31 0.932 29

0.70 7

0.89 7

0.857 27

0.93 4 0.86 5

0.04 11

0.70 7 0.984 8 0.993 2 0.581 31 0.932 29 -Co.15 >0.982 >0.94 0.912 36 0.86 5 >0.976 0.879 25 0.857 27 >0.94 >0.95 0.89 7 22 5 27 6 <8 <7 21 14

65 30 3.1 15 1.45 99 18 13 6 >600 <3 ~8 17 8 27 II <4

Measured F-values have been converted into those for E, = 992 keV and for 20 +g/ cm* target thickness. A 15% systematic error has been added in quadrature to the statistical error. Value to appear in the 1990 A = 21-44 evaluation (Endt), as the weighted average of six values with errors below Ref. 38). ‘) Ref. “). ‘) Ref. 36). Weighted average of values in refs. 39*40). Ref. 39).

9165 9316 9382 9417 9479 9702 9765 10182 10209 10418 10596 10668A 106686 10725 10900 10944

40 fs.

22 7 0.72 11

10 3 14 4 26 5 0.48 8

6000 2000

447 10 5 105 135 25

0.90 16 “) 0.126 12 “)

0.56 1 I “)

37 5 r)

230

P.M. Endt et al. / Spectroscopic

information

The agreement of the present lifetimes with those from previous work is generally good. This does not apply e.g. to E, = 4.98, 6.88, 8.33 and 8.41 MeV, but it should be kept in mind (partly rather factor of two. Arguments states

measurements

for J”; T assignments

(see table

available.

that the lifetimes

early)

6) are included

listed

in ref. “) for these levels are averages

showing

large

mutual

differences

of

of up to a

to **Si levels are shown in table 12. All secondary for which

For 16 levels the new assignments

new information, or restrictions

relative

to ref. 6), is

result partly or altogether

from the present work. The ground-state transitions with b(y) = (2.2 Z)% and (1.5 2)% observed at the J”; T = 2-; 0 E, = 655 and 760 keV resonances, respectively, are disturbing. They have M2,s character, both with a strength of 0.17 W.U., such that they exceed the RUL of 0.1 W.U. [ref. “)I. The lines do not originate from the instrumental tail of a lower-energy resonance, from the Breit-Wigner tails of neighbouring broad resonances, or from direct capture. Nor is it probable that the resonance wave functions contain significant T = 1 admixtures, because the nearest J”; T = 2-; 1 resonance is far removed, at E, = 1520 keV. The latter is the analogue of the level in **Al, at E, = 3.88 MeV. The resonance J”; T values are quite through the y-decay. The RUL listed in ref. ‘*), however, is not so (based on only eight transitions) and we conclude that it should

lowest-energy 2firmly established firmly established be increased.

The new doublet at E, = 10.67 MeV is rather remarkable. We assume that at the E, = 992 and 1317 keV resonances different components of the doublet are excited at E, = 10 668.05 7 and 10 668.34 4 keV, respectively, here denoted as 10 668* and 10 668’. The excitation at E, = 767 keV is not strong enough to provide relevant information. The assumption of doublet character is largely based on the different y-decay observed at the 992 and 1317 keV resonances and shown in table 8. The decay is seen to be definitely different but not strikingly different. None of the decay lines (except for some of the very weakest) can be placed anywhere else in the resonance decay schemes, nor can any be interpreted as escape lines or be attributed to known contaminants. The decay lines which are strong at one resonance and weak or absent

at the other can be used to investigate

in how far the decays at the

two resonances really originate from single states. If this is true for the 992 keV resonance, then 10 668* can at most contribute 25% to the decay at the 1317 keV resonance, whereas 10 66gB cannot contribute more than 14% to the decay at 992 keV. The lifetimes of the two states are the same within the combined error (table 11). The energies are not quite the same (table 9) but the difference, 0.29 8 keV, is only barely statistically significant. No systematic differences could be found for the energies of decay lines to different levels. By Meyer et al. 17) transitions to a 10 668.8 24 keV level (regarded as a single state) have been observed at the E, = 1317 and 1381 keV resonances with primary branchings of 4.0% and l.O%, respectively. The decay of this level as given in ref. i7) is also shown in table 8. It resembles most

P.M. Endt et al. / Spectroscopic information TAkXE

231

12

Arguments for J”; T assignments to z8Si levels “) Other refs.

y-decay

y-feeding

Resulting assignment

8945 9165 9417 97&S* 9796 9929 X0190 10209* 10311 10418 10540 10668A’ 10668e* 1os33* 10916 10944” 10951* 11079”

(4’9 5-) (3”“,4+) (2+, 3-, 4+) (2, 3) (2-4+) (1,2)_

5’ b) 4+ ‘) 4+ b) +2-

(2-4)+ d,

t’4+

5- ‘) (2+-4’) (2*-4*) “+ (t-34-) + I (G-4+) N:Oh)

(1,2+)

(O-5)+ ‘) 5+ b) (i-4)-‘) C&3)+ ‘)

C&3)*; (I) rt;O

(l--4+) (2+-4+); 0 +. (04,:4:)

2; o+ I ‘)

6+‘)

(1,2? (1,2? fo+-4’) (2+-4+) (I-, 2+) (o+-4+) ;t ;OC)

(1+-r+) (324) (2+,‘3); I 4’;O

(2*-4-)

(2, 3); I*)

(X3)+ ‘)

11195”

11265* 11433 1143s+ 11509”) 12174” 12318* 12324* 12541* 12854”

(1, 27 d, (1,2’+) “)

(2+-6+) (2+-4-) (2-4) (2-4); 0 (2+-4); 0 (I-3) #4^ ‘) (3-5)

(2,3)+j)

T=O, t(2+ 4’ f2+ ;I

5+ 4+ 4+ 32+ 152+ (Z-4)+ 5+ (l-3)_ (2,3)+; 0 4f; 0 (2,3); 1 2+ 2+ 2+ (2-4+) (2*-4f); 0 2+;0 2+;041 4+; o+ 1 6+; 0 (3-5+) 22; 0 4+ 3+; 1 4+; o+ f

“) For E,, see table 9 and ref. 6f. The J”; 7’ assignments for levels marked with an asterisk partly or altogether result from the present work. For several levels with unknown lifetime the J” restrictions in the column “y-decay” are based on the rule that the decay of states at relatively high E, proceeds through Ml, El or E2 transitions. “) Ref. 37). ‘) Ref. 36). d, Ref. I*); the existence of the ye decay on which the f” = (I, 2’) restriction is based, is ambiguous. ‘) Ref. 6). ‘) Ref. 4’). s) Present work and ref. I’). ‘) The T = 0 assignment of ref. 6, was found to be unjustified. ‘) Ref. I’). j) Refs. 42*43).

the decay of our 10 66SB level but the agreement is certainly not very good. Anyway it is unknown which of their two resonances provided the main information for the 10.67 MeV decay. The existence of the doublet at E, = 11.43 MeV had already been indicated in ref. *7).

232

5. Shell-model calculation; discussion of T = 1 states A shell-model calculation for A = 24 and 28 has been performed in the untruncated sd shell with A - 16 nucleons in the Id,,, , 2~~ and Id,,, orbits. The single-particle energies z(ld& = -3948 keV, E(~s& = -3164 keV and E(ld& = 1647 keV and the 63 two-body matrix elements (taken proportional to A-o.3) have been obtained from a fit to the experimental energies of 447 states in the A = 1’7-39 region with an average deviation of 185 keV [ref. “)]. The results are shown in figs. 2-5. For the T = 1 states in 24Mg and 28Si a comparison is also possible with the parent states in 24Na and 28Al, respectively. For J” assignments to 24Na and 28A1levels, and for J”;T assignments to 24Mg and ‘*Si levels which are not discussed in the present paper, we refer to the 1990 A = 21-44 evaluation (Endt). We start with the T = 1 states for A = 24, shown in fig. 2. All known 24Na states are given, all 24Mg states which have or are assumed to have T = 1, and theoretical A =24 T = 1, r = -I- states up to the energy of the 6:. There is a one-to-one correspondence between 24Na parents and their 24Mg analogues (for one exception, see below) and, for 7r =f, between either of these groups of levels and their theoretical counterparts. The 24Mg E, = 9828 and 9968 keV levels should be regarded as the split analogue (with mixed T = O-i-1 character) of the 24Na 472 keV level. The progress made in the last ten years in the spectroscopy of A = 24 nuclei can best be illustrated by the fact that in the 1978 review “) for only four 24Na levels the analogues in 24Mg could be indicated with any certainty. There are several parent-analogue pairs in which, for one or both of the components, J”; T has not been determined unambiguously. The 12 996 keV 24Mg level, with nothing known about J”;T, is an extreme case. That this level yet can be considered as the analogue of the 3628 keV 3+ level of 24Na is based on the correct Coulomb shift of 148 keV and on the fact that in the E,(24Mg) = 12.74-13.14 MeV region none of the other known levels can have a J” = 3+ assignment. The 10 731 keV 24Mg level is seen to have the “wrong” T-assignment (T = 0). This does not exclude the possibility, however, that the state actually is of mixed T = O-i-1 character. The level has been seen as a very weak resonance in the ‘*Ne( a, y)24Mg reaction “), which establishes the existence of a T = 0 admixture. The lifetime of T, = 10 4 fs [ref. ‘“)I leads to an Ml strength of 29 mW.u. for the main 10.73 + 1.37 MeV, 2’ + 2+ decay. With the RUL for Ml IS transitions being 50 mW.u,, we see that T = 1 character is certainly probable although the transition is not quite strong enough to definitely establish the T = 1 component. There is a single state in 24Mg, the 4+; 0 + 1 level at E, = 13 050 keV, corresponding to the theoretical 4: level, for which the parent in 24Na, expected at E, = 3.7 MeV, is missing experimentally. The reaction with which the 24Na level scheme has been investigated with the highest energy resolution is thermal neutron capture, but with the capture state having mainly J” = If character 23) one would hardly expect a J” = 4+ level to be populated.

P.M. Endt et al. / Spectroscopic

information

233

E (24Na)(MeV) x

Ef4Na)(MeV)

1886

3’

1846

2+ \n3l4

3.7 (3,4)+ 11200 zon

+

0

9516

24Na EXPERIMENT

+ 23

4’

4+;1

24

24M9 T=l

-

THEORY

Na EXPERIMENT

T=l

THEORY

Fig. 2. Isospin triplet states (T= 1) in 24Na and 24Mg as compared to the results of a shell-model calculation. Note the different energy scales for the left- and right-hand parts of the figure. The parent in 24Na of the 13050 keV 4*; 0+ 1 24Mg level, corresponding to the 4: theoretical state, is missing experimentally.

234

P.M. En& et al. / Spectroscopic information

The experimental Coulomb energy shifts relative to the lowest T= 1 state are seen to be remarkably constant, if the shifts for the three A = 24 7~= - levels are left out of consideration. The relatively large downward shifts for negative-parity levels are explained in ref. “). For the positive-parity levels the average shift, A,,={EX(24Na)-EX(24Mg, T=l)},,, amounts to +97 keV, and the average absolute deviation from the average shift amounts to IA -A,,[.. = 43 keV. This number can be compared to the A = 26 case where we found ]A -A,,/,, = 36 keV for the T = 1 states of ‘%Ig and 26AI [ref. ‘)I. This small spread helps to increase our confidence in the proposed parent-analogue correspondences. An analogous comparison can be made between the energies of 24Na states and their theoretical counterparts. For A = E,(24Na) - E,(theory) we find A,, = +155 keV and IA -A,&, = 117 keV. For A = 26 the analogous (latter) quantity amounts to 100 keV [ref. 9)]. In fig. 3 the T = 1 states in **Al and %i are compared mutually, and with their theoretical counterparts. The parent-analogue correspondence for A = 28 (with 33 pairs) is even better than for A = 24 (25 pairs). For all theoretical T = 1 states up to and including the 5: a corresponding experimental parent-analogue pair can be indicated, except for the 3: of which the experimental counterparts are to be sought in energy regions which both in **Al and in 28Si have been badly investigated. Just as for A = 24 there is a single state, the 12 854 keV 4+; 0+ 1 level of 28Sicorresponding to the 4: theoretical state, for which the parent in “Al (expected at E,=3.6 MeV) is missing expe~mentally. Its non-observation can be made plausible by aImost the same argument as given for the missing 4: in 24Na. For the Coulomb shifts, A = E,(“Al) - E,(‘sSi, T = l), we find A,, = +74 keV and /A - A,&, = 46 keV. The differences between the energies of **Al levels and of their theoretical counterparts, A = EX(28Al)- E&theory), average to A,, = 175 keV with an average absolute deviation )A -A,&, = 110 keV. A comparison of experimental and theoretical T =0, V= +, states in 24Mg and 28Si is less rewarding. On the one hand the experimental knowledge about T =O levels becomes increasingly defective above E,= 10 MeV, on the other hand the theory seems to represent in particular the O+; 0 and 2+; 0 levels in a rather poor way, The T = 0, w = f, levels of 24Mg are shown in fig. 4. The energy differences A = EX(24Mg)- E,(theory) of -1129 and f551 keV for the 0: and 0: levels are larger than for any other pair of experimental and theoretical states. No 2+ states have been drawn in fig. 4 above E, = 9.0 MeV because it is uncertain which of the two 24Mg 2’ states at 9004 and 9284 keV should correspond to the theoretical 2: at 9876 keV. For the states shown in fig. 4 we find A,, = -103 keV and )A -A,&,, = 205 keV, the latter number about twice as large as for the T = 1 states (see above). The situation for the T = 0, r = f levels in ‘*Si (shown in fig. 5) is slightly better than for 24Mg, but also here defects are conspicious. The 0: and 0: states are missing experimentally. Only a few out of the many experimental 2+; 0 levels have been drawn above E, = 9.7 MeV. This makes the correspondence with experimental levels

P.M. Endr et al. / Spectroscopic

235

informalion

E (*%l,(M&, x

j-

3.5

3<

2.

2.

4.2 1623 ,620

2* ,‘\10900

1’;l

1 .5-

I 10376

3+:1

10272

O+;l

3.8

1.o972 1014

0’

3q

3’ ,

t

3.6 t C).5 -

349382 ,I-

31 0

2’:l

2+/ 3’

31+ 9316

3+;1 21+

EXPERIMENT

28Si

28Al

28Si

‘%

T=l

THEORY

Fig. 3. Isospin triplet states ( T = 1) in 28AI and *“Si as compared to Note the different energy scales for the left- and right-hand parts 12854 keV 4+; 0+ 1 *sSi level, corresponding to the 4: theoretical experimental counterparts of the 3: (indicated with a flag) are both in 28A1 and in **Si have been badly

EXPERIMENT

T=l

THEORY

the results of a shell-model calculation. of the figure. The parent in “Al of the state, is missing experimentally. The to be sought in energy regions which investigated.

236

P.M. Endt et al. / Spectroscopic

information

Ex(MeV)

7-

5-

_

6010

4+

l

---._

5235

3*

4238

2+

_ 4123

4+

42

31*

-

8655

2*/

8439

4*

* 43

2; 1369

2’1

6, 8113

6*/

5. 7812 (4:5x+)/ 7747 0‘

Oi 24

M9

Fig. 4. Experimental

and theoretical

I.,*

1+

24 ~PERIMENT

*

T=O

Mg THEORY

EXPERIMENT

T=O

THEORY

T = 0, T = + states of *4Mg. No 2+; 0 states have been drawn E, = 9.0 MeV.

above

I? M. Ertdt et al. / Spectroscopic information

28si

“Si ~~RiME~T

T=O

237

THEORY

EX~RIME~T

T=O

%i WEORY

~~E~lM~~T

T=O

THEORY

Fig. 5. Experimental and theoretical T = 0, T = f states of %i. For the 0: and 0: states (indicated with a flag) no experimental counterparts are known. Only a few out of the many experimental 2+; 0 states above E, = 9.7 MeV have been drawn.

238

P.M. Endt et al. / Spectroscopicinformation

shown A =

for the 2:,

-1222

2: and 2; states at least hazardous.

keV for the 3: is disturbing.

in 24Mg and **Si 2+; 0 intruder 2+; 0 and possibly of the sd-shell

states start coming

also O+; 0 a shell-model

the large value

that at E, = 9 or 10 MeV

in, such that at such energies

calculation

only considering

for

the orbits

loses its value.

6. Reaction energies for 23Na(p, y)=Mg The present

And finally

One might conclude

determinations

of the excitation

energies

and *‘Al(p, y)*%i of many 24Mg and *‘Si levels

(tables 4 and 9) have not been performed with all precautions ments, but in principle the Q-values for the (p, -y) reactions be derived from them, and it is interesting on the 1985 table of atomic masses 26).

to compare

of precision measureon 23Na and *‘Al can

them with the Q-values

based

We start with the 27Al(p, y)2xSi Q-value. Several precision measurements exist of the proton energy of the 992 keV resonance with a weighted mean value given in the 1978 evaluation 6, as E, = 991.88 4 keV. Averaged with the recent value E, = 991.843 33 keV of ref. *‘) one obtains E,= 991.858 25 keV. Combined with the value from table 9 for the excitation energy of this level, E, = 12 541.31 14 keV, we find to be compared with Q = Q = 11 585.18 14 for the *‘Al(p, y)*‘Si reaction, 11 584.6 3 keV from the 1985 mass table 26). The 1985 mass table *‘Al(p, y) Q-value is almost entirely based Maas et al. 28), Q = 11 584.5 4 keV. For the y-ray energy calibration the energies

of 66Ga lines given by Heath 29). Recent

more precise

on the result of the latter used 66Ga measure-

ments 30) have shown that the Heath energies are slightly too low. The corresponding correction increases the Q-value of ref. *“) and thus also of ref. 26) by 0.32 keV. Our Q-value is thus in perfect agreement with the corrected mass-table value, the difference amounting to +0.3 3 keV. E, = 1417 keV resonance For the 23Na(p, y)24Mg Q-value only the (narrow) should be considered because the E,= 1020 and 1318 keV resonances have rather large natural widths of r = 4.0 5 and 2.5 2 keV, respectively I’). The proton energy of ref. 3’), E, = 1416.79 7 keV, corrected so as to bring the energy of their *‘Al(p, y) calibration resonance to the value E, = 991.858 25 keV mentioned above, combined with our resonance excitation energy E, = 13 050.22 14 keV (table 4) results in a Q-value Q = 11692.97 17 keV to be compared with the mass table *“) value Q = 16 690.8 6 keV. In this case it is not easy to trace which links between the 23Na and 24Mg masses have been used to arrive at the Q-value of ref. 26>, such that the difference of -2.2 6 keV with our Q-value cannot easily be explained. Again, we do not pretend that our energies can be interpreted as resulting from precision measurements. In particular the error in the 90” detector positioning (see sect. 4) is not accounted for in the error AQ of our 23Na(p, y)24Mg Q-value. For a positioning error A0 = 0.5” we may estimate AQ as follows. The resonance E, value has been determined through the primaries to the E, = 9.46 and 10.581 MeV levels, which in

P.M. Endt et al. / Spectroscopic

turn

decay

through

6.01 MeV secondary i.e. they have F(7,) from

9.46+

1.37, 4.12 and

6.01 MeV and

10.581+ 4.24, 5.24 and

transitions. These eight lines can be assumed to be fully shifted, = 1. The calibration curve, based on lines with F-values ranging

F(T,,,) = 0.05 for the 1.37+ 0 MeV transition

1.37 MeV line,

239

information

is thus split up in parts

to F(r,,,) = 0.80 for the 4.12+

with different

“local”

Each of the eight lines mentioned above then contributes by an amount proportional to { 1 - F( T,),,,}E, multiplied

F-values,

F(T,,,),,,.

to AE, (and thus to AQ) with the relative weight

which the line has in the determination of E,. The sum of the contributions is equal to AQ = 0.07 2 keV for A@ = 0.5”, an amount which is far too small to explain the difference

between

our Q-value

7. Nucleosynthesis

and that of ref. 26).

with the *‘Ne(cu, y)=Mg

and 24Mg((u, y)**Si reactions

The present investigation has provided information on levels close above the a-particle binding energy, which thus possibly are of importance for nucleosynthesis with the (a, y) reactions on 20Ne and 24Mg. to E, = O-2000 keV are listed The levels in 24Mg corresponding thorough

search

for “Ne(a,

y)24Mg resonances

in the region

above

in table E,

=

13. A

550 keV

has been performed by Schmalbrock et al. I*). Levels with unnatural parity cannot be expected to resonate, and T = 1 levels can only do so through a possible T = 0 admixture. The levels at E, = 9528 and 10 028 keV could resonate in principle but the corresponding high cY-particle orbital angular momenta, 1, = 6 and 5, respectively, would severely reduce the penetration through the Coulomb barrier. The 9533 keV level might be a candidate for resonance character, but the possible contribution cannot be estimated as long as J” has not been determined unambiguously. The same holds for E, = 10 161 and 10 581 keV, and for the 10 660 keV doublet, but the corresponding S( CX,y) upper limits already show that the ( LY,y) contributions from these levels would be very small. The levels in **Si which possibly could contribute to the 24Mg(a, y)*‘Si reaction for E, < 2000 keV are shown

in table

14. Only six out of the 37 levels listed have

been observed as (a, y) resonances “). Another 19 levels with certain or possible N; 0 assignments are candidates for resonance character. A new search for weak resonances with all possible measures taken to reduce background, in the spirit of ref. 12), might well be rewarding. Because the energies of resonance candidates are known with keV precision, such a search could be concentrated on relatively few small energy regions. Evidently additional spectroscopic information on the E, = 10.0-11.7 MeV region in 28Si obtained with other reactions would be equally welcome. 8. Conclusions The present measurements of good y-ray spectra at a small number of (p, y) resonances are of a simple nature. Yet they have provided a relatively large amount

P.M. En& et al. f Spectroscopic information

240

TABLE 13 Nucleosynthesis

with the “Ne(cw, y)24Mg reaction “) J”;T

Exb) UceVl

175 245 259 265 619 787 859 897 959 1019 1227 1259 1517 1523 1618 1618 1642 1680 1703 1811 1926

9458 9516 9528 9533 9828 9968 10028 10059 10111 10161 10334 10361 10576 10581 10660A 106608 10680 10712 10731 10821 10917

63 15 7 16 7

ref. 6,

present

(2-4)+ 4+; 1 6+

3+(2+) d, 4+; 1 6+; 0 *)

1+;(1)

0.410 85 90 2.5 <4

1+; 1 5; 0 (1,2)+; (1) 0+ 4+

2.1 5 13 3

I

<3

-

0.034 3 10 4

sta,

(2-4;:

1

(l-4+)

Of; 0

1+; 1 (l--3+) 2+;0

(273); 0 1+; o+ 1 1+; 1 5; 0 2+(1+); 1 df o+; 0 (0,l)’ 3-; 0 2+; 0 5+(3+); 0 (3,4+) (l-3_) (3,4)+

o+; 0 1+; 1 2+;O+ld) 3+; 1 d) 2’; 0

Y) ‘)

Imevl


<0.08 <0.08 0.29 6 (0.08 0.30 6 0.48 10

I

<0.2 co.2

I 17020 2.6 5 co.2 2200 300

“) All levels corresponding to E, < 2000 keV are listed. Entries in columns 2, 3 and 5 are from the present work or from the 1990 A =21-44 evaluation (Endt). b, As calculated from I?, with Q(a, y) = 9311.8 19 keV [ref. r6)]. “) From ref. ‘r) if not mentioned differently. d, The present shell-mode1 calculation has also been used; see figs. 2 and 4. “) Calculated from the relation S( CY,y) = (2J -I-l)r,f,/r <:(2J + l)r, with I’ derived from T_.

of new information on y-ray branchings, excitation energies, lifetimes and J”;T values for two nuclei which were already among the best studied of the sd shell. Evidently an extension of this work to more resonances may lead to pretty complete level schemes of 24Mg and 28Si (including states with spins up to about J = 6), just as our recent investigation 2*3S9) of the “Mg(p, T)~~ALreaction at 75 resonances has clarified the 26Al level scheme. The present detection of several previously unobserved levels, all components of close doublets or triplets, came as somewhat of a surprise. It shows more than anything else the advantages of (p, -y) work at several (preferably many) resonances with good energy resolution and with accurate energy determinations included. The shell-model calculation has substantially contributed to the interpretation of the observed level schemes, in particular for T = 1 states. For levels with non-unique J”; T assignments it helps to select the correct value out of several possibilities,

P.M.

Emit

et al. / Spectroscopic infarmntion

241

TABLE 14 Nucleosynthesis

with the z4Mg(cx, y)*sSi reaction “)

J";T

Jz% bl EkeVl 231 240 262 336 381 457 506 618 648 714 798 798 864 958 1049 1068 1087 1120 1128 1178 1277 1301 1346 1413 1494 1529 1571 1638 1690 1693 1705 1779 1786 1854 1868 1952 1965

ref. 6, 10182 10190 10209 10272 10311 10376 10418 10514 10540 10596 10668* 106688 10725 10805 10883 10900 10916 10944 to951 10994 11079 11099 11138 11195 11265 11295 11331 11388 11433 11435 11446 11509 11515 11576 11585 11657 11669

<8 <30 154 (60 16 6 265

0.56 II 22 5 25 5 0.90 16

3.’ (2+-4*) (0, l).“; 1 (2+-4+) 3+; 1 3+ (1.-_4!; 1+; o-t 1 3+ 1+;0+1 (F-4:;

0.126 I2

1+; 1 N;O

21 14

Cl5 2+; 0

1-; 0 <30 (30 50 30 0.0280 14 <30 340 zoo

C&3)+; (1) 4; 0 1+; 1 2+; 0 6-; 0 3-; 0 2+; 0 1-;o

S(a, Y) present

Emevl

352+ 0’; 1 3’(2+, 4+); Od) 3+; 1 5+; 0 d) + (I-3:1+; o-l- 1 C&3)+; 0 4+;0 1+; o-f- 1 2+ 2”(2_, 3); 1 d) 1+; 1 2+ 2+ 2+ (2-4’) 6+; 0”) f. (*+-4$8 2+; 0 1-; 0 6+; Od) 2*:0+1 4+; o+ 1 1+; 1 6+; 0 2’; 0 6-; 0 3-;O 2+; 0 i-; 0

<40 “) ~60 “)

<40 “)

1.9 6

11020

130

60 10 40 10 140 30 330 70

“) All levels corresponding to E, < 2000 keV are listed. Entries in columns 2, 3, 5 and 6 are from the present work or from the 1990 A = 21-44 evaluation (Endt). b, As calculated from E, with Q( cy,y) = 9984.2 4 keV [ref. 26f]. ‘) See table 13, footnote “). d, The present she&model calculation has also been used; see figs. 3 and 5.

242

P.M. Endt et al. / Spectfoscopic informarion

and it has convincingly proven the existence of experimentally missing 4+ levels in both 24Na and 28A1. For the understanding of the T = 0 level schemes of 24Na and “Si at excitation energies above about sd subshells are taken into account.

10 MeV the shell model fails if only the three

As stated already in the Introduction this paper presents the analysis of (p, y) spectra originally measured, on the initiative of C. van der Leun, with the purpose of providing F.P. Jansen, ments.

intensity calibrations of Ge detectors at high y-ray energy. We thank F. Hallebeek and H.J. van Wijk for their assistance with the measure-

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B. Zwieglinski, GM. Crawley, H. Nann and J.A. J.R. Vanhoy, E.G. Bilpuch, CR. Westerfeldt and F. Glatz et aZ., Z. Physik A303 (1981) 239 F. Glatz et al., 2. Physik A324 (1986) 173 J. Dalmas and G.Y. Petit, Can. J. Phys. 56 (1978) R. Schneider et a/., Nucl. Phys. A323 (1979) 13 U.E.P. Berg et al., Phys. Lett. B140 (1984) 191 H. Nann, Nucl. Phys. A376 (1982) 61 A.E. Champagne et al., Nucl. Phys. A459 (1986) R.O. Nelson, E.G. Bilpuch, C.R. Westerfeldt and (1984) 755 44) B.H. Wildenthal, Progress in Particle and Nuclear 45) E.O. De Neijs, M.A. Meyer, J.P.L. Reinecke and

243

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917

239 G.E. Mitchell,

Phys. Rev. C29 (1984) 1656; C30

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