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High-spin states in the N = 50 isotones 91Nb and 93Tc populated in (α, p2nγ) reactions
1.E.I:2.B I
Nuclear Physics A212 (1973) 429--447; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilmwithout written permission from the publisher
H I G H - S P I N S T A T E S I N T H E N = 50 I S O T O N E S 91Nb A N D 93Tc P O P U L A T E D I N (~,, p2nT) R E A C T I O N S M. GRECESCU t, A. NILSSON and L. I-[ARMS-RINGDAHL Research Institute for Physics, 104 05 Stockholm 50, Sweden Received 27 December 1972 Abstract: The reaction (ct, p2nT) on 9°Zr and 92M0 targets was used to populate excited states in 9tNb and 93Tc, respectively. The de-excitation of these states was studied by in-beam ),-ray spectroscopy. The ~,-ray transitions belonging to these nuclei were identified by studying coincidences with charged particles, excitation functions and )'-7 coincidences. Angular distribution and lifetime measurements were also performed. Many new levels were observed, particularly in 9aTe. They are interpreted in terms of shell-model calculations as belonging to the (g~r)3 and (P~r) (g~_)4proton configurations.
E
NUCLEAR REACTIONS 9°Zr, 92M0(~, p2n~,), E~ = 37--43 MeV; measured E~,, 1~, (Ec~, 0) tiT'-delay, pT-coin., ~,7-coin. 9lNb, 93Tc deduced levels, J, ~z. Enriched targets. Ge(Li) detectors.
1. Introduction D u r i n g recent years, several theoretical and experimental investigations have been devoted to the properties o f multi-particle states belonging to a multiplet configuration ( j ' ) or to the associated configurations {(jn),jl = ½}. K h a r i t o n o v et al. 1) have pointed out the correlation between the level structure o f these configurations and the properties o f residual nuclear interactions. The experimental studies have been confined mainly to p r o t o n multi-particle states in nuclei with a magic n u m b e r o f neutrons. E.g., in the region of N = 126, Bergstr6m and co-workers 2,3) have studied the following configurations: (~zh~)2 in 21 Opo ' (nh~_)3 in211At and (nh~)3 (vp~r)-i in 21 OAt . In the region o f N = 50, the (r~g~) 2, {(ng~)3(np½)} and (Trgl) 4 configurations in 92M0 and 94Ru, respectively, have been studied both experimentally and theoretically 4, 5, 24). In the same region it would be interesting to establish experimentally the level structure o f the (~g~)3 configuration which can provide information about the parameters o f central and tensor residual interactions 1). The (ng~)a configuration can be f o u n d in 43Tcs 93 o- The g r o u n d state o f this nucleus m a y be regarded as consisting o f the {(7~p~)2(rcg~) a} configuration outside an inert t Present address: Institute for Atomic Physics, Bucharest, Romania. 429 October 1973
430
M. GRECESCU et
aL
aS~Srso core s). It is reasonable to expect among its excited states a number of seniority-three states due to the three g~ protons. The highest spin obtainable in this way is 21_. Negative-parity states are also expected in 93Tc due to the promotion of one p~ proton to the g~ orbital. Up to the beginning of the present investigation, the experimental knowledge of the level structure of 93Tc was confined to low-spin states of single-particle type populated in (3He, d) reactions 6, 7) or in the decay of isobaric analogue states a). Recently, studies have also been made by means of (d, n) reactions 9) and (ct, t) reactions 1o). The lowest excited state is a ½- isomeric state at 393 keV with a halflife of 44 rain [ref. 11)]. The population of 93Tc levels in the radioactive decay of 93Ru (T~ = 63 s) was virtually unknown. The level structure of 91Nb has been investigated by stripping and pick-up reactions 6, 12, ~3), by the radioactive decay of 91Mo and 91raMo [ref. 14)], and by the (P, 7) reaction is). It has also recently been studied by means of the (p, nT) reaction ~6, ~7). The lowest excited state is a ½- isomeric state at 104.5 keV with a halflife of 62 d. The (~zgl_)3configuration should appear also among the excited states of ~lNb5 o by raising the p½ proton pair to the g~ orbital. The previous considerations prompted us to start an investigation of high-spin states in 93Tc and 91Nb, populated preferentially by nuclear reactions with eparticles. A preliminary report of this work has been published previously 19).
2. Experimental procedure 2.1. TARGETS AND REACTIONS The excited states of 9aTc and 91Nb were obtained via the (0t, p2n~) reaction on
92Mo and 9°Zr isotopes. The Mo target consisted of 10 mg Mo powder, enriched to 98.3 7o in 92Mo; the Zr target consisted of 13 mg ZrO 2 powder enriched to 97.6 in 9°Zr. The targets were prepared by depositing the powder between two Formvar foils of 150 mg[cm 2 each. The mean target thickness was 10-20 mg/cm 2. The (~, p2n) reaction occurred simultaneously with the (~, 3n) reaction when bombarding the targets with an ~t-particle beam having an energy between 37 and 43 MeV. The strong competitiveness of the (~, p2n) compared to the (~, 3n) reaction is due to the low binding energy is) of the proton compared to that of the neutron in the considered region of neutron-deficient nuclei. For example, in the case of the 92Mo target, the Q-value of the (~, 3n) reaction is -33.02 MeV whilst that of the (cq p2n) reaction is -26.06 MeV and the Coulomb barrier for the proton is about 7 MeV. The results concerning the nuclei produced by (~, 3n) reactions on 9°Zr and 92Mo are presented in an accompanying paper 20). The s-particle beam with a maximal energy of 43 MeV was delivered by a fixed frequency cyclotron with a 225 cm pole diameter. The energy was lowered stepwise by introducing degrading foils at a focal point in the beam transport system.
HIGH-SPIN STATES (I)
431
The geometry of the experimental arrangement is described in previous publications 21,22) from this laboratory. 2.2. ENERGY, INTENSITY AND A N G U L A R DISTRIBUTION MEASUREMENTS
The y-radiations were detected with a 40 cm a coaxial Ge(Li) detector ( F W H M 2.5 keV at 1173 keV) and a 5 mm thick planar Ge(Li) detector for X-rays ( F W H M 650 eV at 122 keV). For the study of excitation functions, the detectors were placed at an angle of 126 ° with respect to the beam direction, in order to reduce a possible anisotropy effect (P2 (cos 126 °) = 0). The spectra were recorded on a 4096-channel Intertechnique pulse-height analyser and they were subsequently computer-processed, in order to determine the positions and areas of the photopeaks. The energy and intensity calibrations of the spectrometer were performed off-beam with a set of radioactive standard sources provided by the IAEA. An in-beam check on the energy calibration was provided by several strong activity lines occurring especially in the irradiation of the 92Mo target. The agreement between our energy values for these lines and recent data from radioactive decay studies is generally within 0.2 keV. We assume that for strong and well resolved lines the errors in the energy and intensity values are less than 0.3 keV and 10 ~ , respectively. A few of the observed y-rays were common to all spectra: 110, 184, 197, 238, 597, 690 and 937 keV; they are due to a-particle reactions on 160 in the targets and to neutron interactions in the Ge(Li) detector 2a). The angular distributions of y-rays relative to the incident beam direction were measured at five angles between 90 ° and 155 °. The normalization of the experimental data was performed by monitoring the beam intensity with two surface-barrier Si detectors mounted symmetrically relative to the beam axis, at angles of + 25 °, in the horizontal plane. The sum of the counts delivered by the two detectors was corrected for the dead time of the multichannel analyser, and was taken as a measure of the total charge incident on the target during the live-time. The normalization procedure was checked with the angular distributions of two known isomeric transitions 24) appearing in the spectra: 148 keV (T½ = 220 as) in 92Mo and 145 keV (T, = 73/~s) in 94Ru; in both cases we obtained the expected isotropic distribution. The experimental angular distributions were fitted by a least-squares analysis to the expression:
W(O)=
coast [1 + A~xPP2(cos 0) + A~,Xr'P4(cos0)].
(1)
In order to convert the experimental values A~,xp to the corresponding theoretical coefficients for complete alignment A~ ax, tabulated by Yamazaki 25), the attenuation coefficients O~k(Ji) = .cakAexplAmax/rlk
(k = 2, 4)
must be known. Unfortunately, in the case of our targets only two ~2 coefficients
432
M. GRECESCU et al.
could be experimentally determined from known pure El and pure E2 transitions without delayed (T½ > 10 ns) components (126 and 1033 keV in 94Ru). Since, however, these values agreed with the attenuation coefficients previously obtained for 95Mo and 97Mo [ref. 26)], we used the latter in the interpretation of our angular distributions. The interpretation was perfolmed along the same lines as described in the appendix of ref. 26). 2.3. LIFETIME MEASUREMENTS The half-lives of delayed y-ray transitions were measured with the experimental facilities described in refs. 27,28). The lower limit of measurable half-lives was determined mainly by the time resolution of the system and was about 10 ns. The upper limit in the ns region was determined by the time interval between successive beam pulses. This interval was normally 125 ns but it could be increased up to 625 ns by using an electrostatic beam deflecting system. For longer half-lives, a magnetic beam pulsing was employed, covering a range from about 10 #s up to a few seconds. A gap existed for half-lives in the decade 1-10 #s, where no accurate measurements could be performed with the available systems. The adopted measuring procedure consisted in taking two-dimensional spectra with 512 energy channels and 8 time channels. The energy region of interest was covered in two steps: 100-900 keV and 900 keV-2 MeV. 2.4. COINCIDENCE MEASUREMENTS 2.4.1. The y-y coincidence measurements were performed with a computer online system 29). Two 40 cm a Ge(Li) detectors were placed in the horizontal plane at angles of about + 135 ° relative to the beam direction and mutually screened. The coincidence system was of the conventional fast-slow type, having a resolving time of about 80 ns, thus eliminating any influence from neighbouring beam pulses with a time distance of 125 ns. The beam intensity was adjusted in order not to deteriorate the resolution of the energy spectra due to high singles counting rate. The true/random coincidence ratio was then well above 10, and the coincidence rate about 200 coinc./s. Each detector was coupled to a 4096-channel ADC. The digital information about each coincidence event was transmitted to the computer and stored on magnetic tape, The main analysis of the data was performed off-line by reading the tapes into the computer memory. By setting gates in the spectrum from one of the detectors, the corresponding coincident spectra from the other detector could be singled out. A maximum number of 32 gates could be set simultaneously. 2.4.2. In order to separate the y-ray transitions belonging to the (~, p2ny) reactions, p-~ coincidences were measured at E~ = 43 MeV. The proton detector was a Si surface-barrier detector with ~ = 5 mm and a depletion depth of 2 ram, placed at about 135 ° with respect to the beam direction. The output of the fast-slow coin-
433
HIGH-SPIN STATES (I)
cidence system was gating the multichannel analyser recording the ),-ray spectrum. Because of the crucial importance of these measurements for the isotopic assignment of ~,-rays, the correct operation of the system was carefully tested. The energy spectra of charged particles emitted by the target were measured for enriched H2Sn and 1248n targets, In the neutron-rich 12¢Sn only (g, xn) reactions occur and the charged particle spectrum corresponds to the g-particles scattered in the target. No elastically scattered g-particles were observed. In the neutron-deficient 112Srt the (g, xn) reactions were known to compete with~ the [g, p ( x - 1)n] reactions a0) and a charged particle spectrum with energies between 3 and 14 MeV and with a typical evaporation shape was obtained. Another test was provided by the ),-ray transitions due to g-particle reactions on 60 (see table 1). Only the lines belonging to (g, p) and (g, pn) reactions were seen in the p-~, coincidence spectra. TABLE 1 Gamma-ray transitions produced by 43 MeV m-particle reactions on x60 in a 9°ZrOz target Energy (keV)
110 197 184 937 238
Reaction
160(g, 160(g, 160(ct, 160(g, 160(g,
p)lgF p)19F pn)laF pn)laF n)t 9Ne
T1. (ns)
I (arb. units) in the singles spectrum
prompt 88 150 150 18
6.8 36 124 151 22
I (arb. units) in the proton coinc, spectrum meas. calc. a) 6.8 8.0 19.6 21.3 0
5.3 8.5 18.5 22.5 0
a) The calculated values (arbitrarily normalized) take into account the time resolution (2r = 90 ns) of the coincidence unit.
The chance coincidence rate was low, so that the y-rays belonging to (g, 2n) reactions in the targets are missing in the proton-coincidence spectra, though they were quite strong in the singles spectra. Since the Si detector was sensitive also to g-particles, the y-transitions in 9 t M o , 199.5, 211.7, 653.8, and 1413.9 keV [ref. 2o)], were found in the coincidence spectrum of the 9 2 M o target, being excited by the 9 2 M o ( g , g'n)~)91Mo reaction. These y-rays were missing in the proton coincidence spectrum of the 9ozr target ' since in that case they were excited by the 9°Zr(g, 3nT)91Mo reaction. 3. Experimental results
A typical spectrum obtained from the 92Mo target at E~ = 43 MeV is represented in fig. 1. It contains about 140 y-ray lines, 25 of them having half-lives > 1 m. The residual y-ray activity of the target has been investigated and the corresponding radioactive nuclei were identified. Their presence shows that at least eight different
"10~!
i
'°I
s3H o
g 7~tSSRu;
F~aX-rays
I
2,oo
~
I
S3Mo
~ ~3~
J
~
~*
~s'oo
i
soo
511
II
m~
CHANNEL
,doo
,o'oo NUMBER
~
I
~Ho
9~H°
3~'oo
18F
,~o
;
2doo
~- particles
,o'oo
Fig. 1. The y-ray spectrum recorded by a 43 cm a Ge(Li) detector at 0 = 126 ° during bombardment of 92Mo with 43 M e V co-particles. T h e lines for which energies, but not nucleide assignment, are given should belong to 93Tc (or possibly 93Ru). A n asterisk indicates lines ascribed to 93Ru.
435
HIGH-SPIN STATES (I) TABLE2 Residual activity of a 92Mo target bombarded with 43 MeV ~-particles Radioactive nucleus
T~
Origin
9°Nb 9°Mo 91raMo 93mMo
14.6 h 5.7 h 66 s 7 h
Decay of 9°Mo (~, ~'2n) (~, ~'n) (¢~,2pn)
9aTe 93mTc 93Ru 94Tc
2.8 44 65 5
94mTc 94Ru 95Tc 95Ru
52 rain 53 min 20 h 1.65 h
h min s h
(e, p2n) and decay of 93Ru (~, p2n) (~, 3n) (c¢,pn) Decay of 9'~Ru (g, 2n) Decay of 95Ru (~, n)
Comments
Not populated in the decay of 93mTc and 9aTe
Not populated in the decay of 94Ru Probably also (~, pn)
reactions occur in the target (see table 2). The relative yields of the (e, 3n), (~, p2n), and (e, 2pn) reactions at 43 MeV are 1 : 11 : 12, as estimated from the intensity of the -~+ -+ $+ transitions in 93Ru, 93Tc, and 93mMo. A picture of similar complexity is found also for the 9°Zr target (about 110 v-ray lines in the spectrum obtained at E~ = 43 MeV). In this case, the relative yield of the (e, 3n) and (~, p2n) reactions is 4 : 1, as judged from the _13+ _~ $+ transitions. The assignment of v-ray transitions as belonging to the (e, p2n) reaction, is based on the following arguments: (a) Shape of the excitation function; in the energy range E~ = 3 7 - 4 3 MeV the excitation functions of the reactions (e, xnyp) with x + y --- 3 are increasing with respect to those of the (e, 2n) reaction. (b) Coincidences with charged particles (see subsect. 2.4.2). (c) Coincidences with v-ray transitions which in turn are coincident with charged particles. This is the case for a few lines which were not observed directly in coincidence with charged particles due to poor statistics. The construction of level schemes for 93Tc and 9 t N b and the spin-parity assignments are based on the following experimental information: V-V coincidences and relative intensities in the coincidence spectra; lifetime measurements; relative shape of the excitation functions; angular distribution data. Besides its use for the isotope assignment, the eXcitation function of a transition can also give valuable indications about the spin of the emitting level. It has to be used quite carefully, however, since at high e-energies it is expected to be rather insensitive in the range of low spin values [cf. fig. 5b in the following paper 2o)], and since weak lines belonging to the next higher isotope may appear in unresolved doublets and make the spin appear too low [cf. the 284.5 keV line in fig. 2 of the following paper].
436
M. GRECESCU et al.
3.1. THE NUCLEUS 93Tc The ~-ray transitions assigned to 93Tc are listed in table 3. The excitation functions for the strongest transitions are represented in fig. 2. The results o f the ~,-y coincidence measurements are summarized in table 4. TABLE3 Gamma-ray transitions from the reaction 92Mo(~t, p2ny)93Tc at E~ = 43 MeV E~, ") I~, Isomeric b) (keV) relative fraction (%) 350.3 523.2 607.5 629.3 680.5 711.0 750.4 1095.9 1434.2 1515.8 1721.9
33 5 28 15 7 28 58 38 100 24 8
2 0 10 72 10c) 73 22 0 40 67 0
Angular distribution A2~ '
0.254-0.01 0.404-0.04 0.294-0.03 --0.154-0.02 --0.474-0.08 0.10-4-0.02 0.124-0.01 0.264-0.02 0.174-0.02 --0.154-0.03 0.404-0.04
Assignment
A.~' --0.084-0.02 --0.084-0.08 --0.094-0.05 0.004-0.03 0.054-0.10 0.004-0.03 --0.074-0.02 --0.104-0.03 --0.024-0.04 +0.114-0.04 --0.064-0.08
2535(-2]L+) -+ 2185(3~-+) 3918(~--) --* 3311(-~-) 2145(-~--) ~ 1516(-~L+) 680(7+) ~ g.s.(9+) 2145(~L-) -+ 1434(-~ +) 2185(3~-+) --* 1434(~- +) 3311(~--) --* 2215(~Z-) 1434(-~- +) ~ g.s.(9+) 1516(.~- +) --> g.s.(9+) 4257(-2~+) --~ 2535(~L +)
Coincident with charged particles yes
yes yes yes (weak) yes yes (weak) yes yes
yes yes (weak) Coincident with 350.3 keV
y-ray transitions tentatively assigned to 9aTc
70.0 707.8 781.2 788.8 835.9
2 2 1 2 1
2215(~Z-) ~ 2145(~--) 2223(~ +) --~ 1516(3~-+) 2215(~--) -~ 1434(~- +) 2223(-~ +) ~ 1434(~- +) 1516(~-+)~ 680(½+)
--0.114-0.08
a) 4-0.3 keV. b) The isomeric parts have 1 /~s < T~. < 10/ts except for the 680.5 keV y-ray. c) 65 s activity populated in the decay of 93Ru. Since m a n y transitions have a p r o m p t and a delayed c o m p o n e n t in the/as range, the values o f the angular distribution coefficients were c o m p u t e d f r o m the data in table 3 with the relation (Aexp~ Zak /prompt ~
exp
ak Iy/I~prompt.
The proposed level scheme is presented in fig. 3. The spin-parity assignments o f the g r o u n d state and o f the first excited state are ~+ and ½-, respectively, according to previous experiments 6).
437
HIGH-SPIN STATES (I) TABLE 4
F-7 coincidences observed in 9aTe Coincidence gate (keY)
350.3 607.5 629.3 711.0 750.4 1095.9 1434.2 1515.8 1721.9
Coincident ?-rays (keV) 350.3
523.2
607.5
629.3
711.0
750.4
yes
1095.9 1434.2 1515.8 1721.9
yes
yes
yes
yes weak
weak yes yes
yes
yes
yes yes weak yes
yes
yes
yes
I¥(E)
100 80 6o
100
\
E¥(keV) 1434.2
13/2~912"
750. ,'.
17/2~13/2"
\\
"-~x \ I \.\ \
/,0 •
"
"
"
20 "------~ lO
,~+
8 6
l r~.{,........~,,~ ~.~,)/+/~'
z,
j+
2
3503 711.0 607.5 1515.8 756.1
2112"-~47/2" 13/2~13/2 ° (25/27~.21/2-) 11/2"-~. 9•2" 4"~2+ (a.,2n)
629.3
13/2~11/2+
1721.9 6805
2512t~21/2" ( 7 / 2 ~ 9/2"
523.2
70.0 707.8
~
(17/2-~-13/2") (15/2"--~11/2*)
f 1
37
39
,',1
43
Eet(MeV)
Fig. 2. Excitation functions of y-rays assigned to 93Tc.
The 680 keV level Since the 680.5 keV ~-ray is the only one accompanying the decay of 9 3 R u [ref. 2o)], it may be assumed to be a transition to the ground state. The character of the angular distribution suggests a IAJI = 1 transition, implying spin values of 5 + or J~-+ for the 680 keV level. These values are also supported by the logft value of 6.5 for the branch of the 9 3 R u decay that feeds the 680 keV level (assuming that the ground state of 9 3 R u is ~ + ) . A }+ assignment would be in good agreement with theoretical predictions 31, 37).
438
M. GRECESCU
25/2"
4257
(25/2")-- I
3918
,2,,I _
et al.
( .....
----
m
3311
2535 2223 2215 (1p.s.~Tl12.40ps) 2185 2145
(
1516 1434
680 393
93
43Tc50
]Fig. 3. Proposed level scheme for 93Tc.
From the angular distribution data, a mixing ratio 6 ( E 2 / M 1 ) = 0.7+0.2 is obtained for the 680.5 transition, suggesting a great MI hindrance. This is to be expected if the 5 + level belongs to the (g~)3 multiplet, as the M1 transitions between the members o f a (j)" multiplet are forbidden 32). "[he 680 keV level was also weakly excited in the reaction 92Mo(3He, d)93Tc [E = 660+20 keV, ref. 6)], in 92Mo(~, t)93Tc [E = 680+20 keV, ref. to)], and in 92Mo(p, y)93Tc [E = 680+ 10 keV, ref. s)], probably due to a ng~ admixture in its wave function 1o). The levels at 1434, 2185, and 2535 keV. The strongest y-ray transition in 93Tc is 1434.2 keV, which can feed only the ground state. The coincidence measurements indicate the existence of a cascade 350.3 keV ~ 750.4 keV ~ 1434.2 keV. The order of the transitions in the cascade is established by the relative intensities in the singles spectra and in the coincidence spectra. The angular distribution data (A2 > 0, A, < 0) are consistent with AJ = - 2 for all three transitions and this fact, together with their prompt character (T, < 10 ns), indicates that 350.3 keV and 750.4 keV are E2 transitions and that 1434.2 keV is quite probably also E2. The following assignments are proposed: 1434 keV (_13_+), 2185 keY (17 +) and 2535 keV (-~-+).
HIGH-SPIN STATES (I)
439
The 4257 k e V level. The 1721.9 keV line is coincident with the 350.3 keV y-ray and precedes it, according to the relative intensities in the singles and coincidence spectra. Its angular distribution indicates that A J = - 2 , and the existence of a Doppler tail that it cannot be an M2 transition [the flight time of the recoiling nuclei is estimated to be less than 1 ps, ref. 20)]. The excitation function is typical for a high-spin state, leading to a spin-parity assignment of ~ + for the 4257 keV level. The 1516 k e V and 2145 k e V levels. The 1434.2 keV line is also coincident with a 711.0 keV line, suggesting the existence of a level at 2145 keV. Another cascade observed in the coincidence measurements, viz. 629.3 keV ~ 1515.8 keV, is obviously de-exciting the same 2145 keV level (within 0.I keV). The relative intensities show that 1516 keV is the ground state transition, originating in a level with the same energy. The angular distribution data clearly favour ~1_+ for this level, the M1 part of the de-excitation being strongly hindered. A weak 835.9 keV line observed in the spectrum is presumably the _11_+ ~ ~2+ transition. The angular distribution of the 629.3 keV transition (A2 < 0) and the absence of a ground state transition suggest the assignment _13 for the spin of the 2145 keV level. This value is also corroborated by the angular distribution of the 711.0 keV line (A2 > 0, A4 ~ 0) which is consistent with a fairly pure dipole transition between two states of the same spin. The non-observation of a direct -13 ~ $+ transition with an energy of 2145.2 keV (relative intensity < 0.5 ~o with respect to 1434.2 keV) proves that this is not an E2 transition and consequently, that the 2145 keV level has spin-parity 1.~-. The absence of the 2145.2 keV M2 transition implies a fully reasonable M2 hindrance 33). The 2215 k e V level. Each y-ray transition belonging to the cascades originating from the .13_- and -~-+ levels contains a delayed component with 1 #s < T~ < 10 #s: We assume that the half-lives are identical and that the -~-- and 1-x7-+ states are fed from the same isomeric state. The absence of a transition from this state to the ~- + level, as well as the observed half-life, suggest a tentative spin-parity assignment of _~_7-z for the isomeric state. A careful examination of the low-energy part of the spectrum (between 30 and 100 keV) with a Ge(Li) X-ray detector leaves as the only possible candidate for the higher-energy isomeric transition a 70.0 keV line. Its excitation function is in agreement with the spin assignment, and the angular distribution is isotropic. Unfortunately, its half-life could not be measured because of the limitations of the measuring system at low energies. Another weak point is the existence of an unbalance by a factor of 3 between the intensity sum of the delayed components of the 629.3 keV and 711.0 keV transitions and the intensity of the 70.0 keV transition corrected for internal conversion [~Xtot = 5.16, ref. 34)]. This unbalance may partly be explained by possible errors in the detector efficiency calibration at low energies, and by the rough estimate of the delayed/prompt ratio in the time measurements. The energy of a weak 781.2 keV line fits within 0.2 keV with a possible M2 transition between the 2215 keV isomeric state and the -~-+ state at 1434 keV. The Weiss-
440
M. GRECESCU et aL
kopf estimate for half-lives gives 2.4 #s (corrected for internal conversion) for a 70.0 keV E2 transition, and half-lives also in the/ts range for 30.6 keV E1 and 781.2 keV M2 transitions, assuming reasonable retardations. In conclusion, we assume that the isomeric state at 2215 keV has a spin-parity of ~ -. The 2223 k e V level. The existence of a 12--s-+state in this energy region is suggested by the theoretical calculations 23) and seems to be supported by the observation o f two weak y-rays at 707.8 keV and 788.8 keV. The sum-energy relations 707.8 + 1515.8 = 2223.6 keV and 788.8+ 1434.2 = 2223.0 keV are in agreement with the expected de-excitation of the 12-Aslevel via the -~+ and -y-+ levels. The fact that the two lines have about the same intensity indicates a high M1 hindrance. Their excitation functions are consistent with the spin assignment but their low intensity prevented their placement to be checked by use of the coincidence spectra. The levels at 3311 k e V a n d 3 9 1 8 keV. A strong cascade observed in the coincidence measurements is 607.5 keV ~ 1095.9 keV. It is almost certainly a stretched E2 cascade, according to the prompt character of the lines and to their angular distributions. The cascade cannot terminate at the ground state because the excitation functions require much higher spins than )~- and ~ for the levels involved. On the other hand, the terminating state must be long-lived, since we do not see any additional coincidences. The most reasonable conclusion then is that the cascade feeds the ~ isomeric state. The excitation functions are in agreement with ~ - and ~s.- assignments for the 3311 keV and 3918 keV levels, respectively. The strong population of the isomeric state is also explained in this way and the side-feedings of the ~7_+ and ~7 - states become similar in strength. A direct confirmation of the placement of the cascade in the decay scheme would require rather delicate delayed coincidence measurements. A 523.2 keV y-ray was seen in coincidence with the 350.3 keV transition. Its excitation function indicates a high spin for the initial state and the angular distribution and lifetime suggest an E2 character. However, the transition was not included in the level scheme because the coincidence measurements did not exclude its placement on top of the 1721.9 keV transition. 3.2. THE NUCLEUS 91Nb The y-ray transitions assigned to 91Nb are listed in table 5. The excitation functions are presented in fig. 4. Because of the relatively low cross section of the reaction 9°Zr(0c, p2ny)91Nb, only six lines are unambiguously assigned to 91Nb. The coincidence measurements show that three of them form a cascade 356.7 keV --* 819.3 keV ~ 2291.1 keV, the order being established by their relative intensities. The angular distributions and the prompt character of these lines indicate that the cascade consists of stretched E2 transitions. The following spin-parity assignments are proposed, supported by the excitation functions: 2291 keV (_x3+), 3110 keV (-~-+), 3467 keV (2--1-+). A level at 2292 keV which is probably identical with our 2291 keV level was observed in the reaction 91Zr(p, ny)91Nb [ref. 16)].
HIGH-SPIN
441
STATES (I)
TABLE5 Gamma-ray transitions from the reaction gOZr(a, p2ny)g1Nb at E, = 43 MeV
E, ‘7 (kev)
1-l
Half-life “)
Assignment
Angular distribution
relative A,‘“P
193.8
65
16 % prompt
A.$==p
0.05&0.02
0
Coincident with charged particles
1984
+ 1790
yes
3467(?-+)
+ 3110(-1_i+)
3110(7+)
+ 2991(?+)
yes yes
1790
+ g.s.(9+) 2
+s4 % (T+ = 120 ns) 356.9
61 ‘)
519.4
98
96 % prompt
1790.4
69
30 % prompt
prompt
0.29 *0.02 d,
-0.10*0.03
0.31*0.02
-0.10~0.03
d)
+4 % long
1984.3
97
0.08&0.03
0.03 10.04
Coincident
+70%
with
(T+ = 120 ns) 30 % prompt
193.8 keV 0.05
i-o.04
0
1984
--f g.s.(F+) 2
2291(=+) 2
-+ g.s.(T+) 2
+70% (T+ x 120 ns) 2290.7
100
87 % prompt
0.21 *to.03
-0.09+0.05
Coincident with
+I3 % long
819.4 keV “) “) ‘) ‘INb d,
&0.3 keV. “Prompt” means T+ < 10 ns and “long” means T+ > 200 ns. The 356.9 keV peak is actually an unresolved doublet; the intensity of the contribution was estimated from coincidence measurements. For the unresolved doublet.
IyE)
Ey keV
Iy(2290.7)-loo LOO -
.-_-_.__------__* *\ \
200 -
.
16139
\
‘\\
,oo - 2%
21964.3 %2
*\ 80 -
\ .
60 - ._.,.i,:
. LO37
39
41
'W 356.9 15095
43 E,.MeV
Fig. 4. Excitation functions of y-rays assigned to 9’Nb.
from
442
M. GRECESCU et al.
21/2"
21/2"
3.70
17/2"
3.32
3~67
17/"2"
3110
13/2+
2291
1984
11/2-,
2.62
1~
2.46
1~2-
2.18
9/2-
192
9/~
0
1790
9/2+H
0
EXPERIMENTAL
CALCULATED
91Nb ,'.1 S0 Fig. 5. Proposed level scheme for 91Nb. The assignments for the negative-parity states are taken from ref. 1s), and the calculated levels which are relevant to the comparison with experimental data are taken from ref. al).
According to the coincidence measurements, another cascade is formed by the 193.8 and 1790.4 keV ~-rays. The cross-over transition 1984.3 keV is also present. The corresponding levels at 1790 and 1984 keV have been observed also in refs. 15, ~~). With our experimental data we were not able to check the spin-parity assignments proposed for these levels in ref. 15). The proposed level scheme for 91Nb is presented in fig. 5. 4. Discussion
Shell-model calculations of 9 t N b and 93Tc energy levels have been performed by several authors a 1, a 5-37) with the following assumptions: (i) only proton-proton interactions in the p½ and g~ 0rbitals are important; (ii) the seniority is a good quantum number in these orbits. Cohen et aL as) proved that the last assumption was almost exactly fulfilled, by calculating the seniority admixtures in the wave functions of several nuclei with N = 50.
HIGH-SPIN STATES (I)
443
"lhe results obtained by different authors are rather similar. We shall follow the calculations of Auerbach and Talmi 31), which are closer to the experimental results. Unfortunately, their calculations are based on obsolete experimental data for the nuclei around 90Zr" For example, the adopted energy values for the excited states of 92Mo, which play an important role in the calculations, exceed the presently known values by 30-50 keV. These differences are obviously reflected in the values of the residual interaction matrix elements. For both 91Nb and 93Tc, the 50 neutrons and the first 38 protons are included in 88 an inert core (3sSrso). The low-lying positive-parity states in 93Tc are due to the (p~)Z(g~)3 proton configuration. It contains the spin sequence from ~+ up to 2~_+, with the exception of a-~+ which is excluded by the Pauli principle. All of the levels belonging to this band were experimentally observed by us, with the exception of three low-spin states (½+, ~-+ and ~+ (v = 3)). There is full agreement between the calculated level order and the experimental results. The calculated energies are slightly higher than the experimental ones. It is interesting to observe that a linear relationship exists between the calculated and the experimental level energies. The relation obtained by a leastsquares fit is: E(fitted) = 69+0.892 E(calc.)A.T"
(E in keV).
It gives an r.m.s, deviation of only 7 keV with respect to the experimental values. The fact that the slope of the line is smaller than 1 can be formally interpreted as a weakening of the interaction when a proton is added to the (g~_)2 configuration. A linear relationship with the same r.m.s, deviation was also found between our experimental data and the levels calculated by Vervier 37), but the agreement is poorer: E(fitted) = 230+0.787 E(calc.)v
(E in keV).
The observed 2s+ level can be interpreted as the highest-spin state obtainable in the (g~)5 configuration. The seniority-five states of this configuration are obtained by raising the p½ proton pair to the g~ orbital and decoupling it. This operation should require an energy of about 2 MeV, judging from the position of the first 2 + state in 9°Zr. This estimate is in good agreement with the observed difference between the 2s_+ state and the highest levels belonging to the (p~.)2(g~_)3 configuration. Among the (g~)5 levels only the 2__5_+level was observed; this is probably due to the fact that it is the only one close to the "yrast" line. All the other levels are probably situated much higher than those having the same spin but belonging to the (gl)3 configuration. The strong cascade observed in the positive-parity band of 93Tc (2_~+ ~ 21_+ 1_~_+ ~ _123+ _~ ~2+) is typical of a de-excitation cascade involving yrast levels. The negative-parity states in 93Tc are due to the (p~)(g~)4 configuration. According to Auerbach and Talmi [ref. 31), eq. (14)] the total energy of a state belonging
444
M. G R E C E S C U et al.
to this configuration is given by the relation:
[flJo E = Cp+4C,+V(g~Jo)+4c~ + [ - / ~ ( J o + l )
for for
J = Jo+½ J = Jo-{,
(2)
where C O = single proton energy in the 2p} orbit; Cg = single proton energy in the lg~_ orbit; V ( g ~ J o ) = (g~Jol Vpplg~Jo> matrix element of the proton-proton interaction in a state with definite spin Jo; ~ = average interaction between the p} proton and the g} proton; ]Y = splitting parameter. As there are no published results about the negative-parity high-spin states in 93Tc, we performed the necessary calculations. /..72
MeV
~58 L5 /.257
25/2 +
3919
(25/2-)-- - - - - - - /
3311
(21/2-)-- - - - -
/
&O
/
2112"
3.87
3.5
2535 2223 27..15 2185 21/,5
1516 1/,34
-
-
15/2"
317
-
-
1112"
2.97
21/2* 17/2" 7/2"
2.76 2.80 2.57
17/2+ 9/2"
2.38 2.26
9/2 +
1.9/,
9/2 + 312-
1.73 1.71
13/2+
1.53
5/2 +
1.33
21/2 + (15/2.)~ ( 1 7 / 2 " 17/2+ - - . - - / / 13/2- ~ "
11/2 + • 13/2 +
)
~
/ /
3.0
20
1.5
1.0
680
7/2 ÷
7/2 +
0.69
393
1/2" ~
1/2-
0.41
9/2*
~
EXPERIMENTAL
O.5
9/2+
CALCULATED
93
~3Tc5o
Fig. 6. Comparison between the proposed level scheme for 93Tc and the results of theoretical calculations. The calculated energies of the positive-parity levels were taken from ref. a,).
HIGH-SPIN STATES (I)
445
The seniority-four matrix elements V(g~Jo) were computed from the V(g~J') valuest given in ref. 31) with the relation: (J"~Jol ~ V~klJ"OtJo> = ½n(n--1) ~. [jn-2(0~ 2 J2)j2(j')Jol}J"~Jo]2(j2J'[Vpp]j2j'>, ~<~ ,2s2s" (3) where
[y-2( 2s2)j (s')Sol}Y :o] are the two-particle c.f.p. [ref. 32)]. The numerical values of the other parameters were also taken from ref. ax). The results of the calculations are presented in fig. 6 together with the positiveparity states and the experimental level scheme. The highest spin obtainable is _~z- for the seniority-three states and ~ - for the seniority-five states tt. In each doublet with J = Jo +½ and J = J o - ½ , the high-spin state has the lowest energy. The level order of the negative-parity states is in agreement with the proposed assignments but the calculated energies are too high. In particular, the 1_~- state should lie about 200 keV lower in order to give to the observed isomeric state. This is quite reasonable because the numerical values of the parameters employed in the calculations are average values for nuclei around 9 ° Z r and r.m.s, deviations of about 100 keV were observed 23). The strong population of the negative-parity band can be explained by the fact that the highest-spin state from the band ( ~ - ) is slightly lower than the -~+ state and thus represents an yrast level. The ground state of 91Nb is mainly due to the proton configuration (p~)2g~ and the positive-parity excited states are due to the (~zg~)a configuration. The excited states are obtained by raising t h e (p½)2 proton pair to the g~ orbital and decoupling it, which explains the big energy gap between the ground state and the positive-parity excited states. The relevant calculated levels are represented in fig. 4 together with the proposed level scheme. Also in this case, a linear relationship was established between the calculated al) and the experimental level energies: E(fitted) = 44 + 0.949 E(calC)A.T"
(E in keV).
Quite recently, the preliminary results of this investigation 19) have been used in theoretical calculations of the positive-parity states in 91Nb and 9aTe [ref. as)]. The main conclusion is that the seniority-three states belonging to the (zrgi) a configuration are fairly pure. 5. Conclusions
Several previously unknown excited states in 9XNb and 93Tc were populated by (~, p2n?) reactions at 43 MeV or-particle energy. Spin-parity assignments were proposed for most of these levels. Many of them are high-spin states (up to ~ - ) t There is a printing error in ref. 31): thus V(gl2 J ' = 8) should be --0.69 MeV. t* We define the seniority of a state belonging to a mixed-shell configuration (jlnO (j2 n2) of identical nucleons as the sum of the seniorities of the various equivalent groups.
446
M. GRECESCU et al.
belonging to the yrast levels. A comparison of the experimental data with theoretical calculations based on the shell model in the seniority scheme confirms that this model correctly describes the level schemes of N = 50 nuclei. Most of the newly discovered levels belong to the (zcg~_)3 or to the (lrp~)(~rg~)4 configuration; they provide a useful experimental basis for more detailed investigations of proton-proton interactions in the 2P½ and lg~: orbitals. The authors acknowledge the cooperation of the 225 cm cyclotron staff during the experiments. One of us (M.G.) wants to express his thanks to Prof. I. Bergstr6m for the possibility of working at the Research Institute for Physics, Stockholm. M.G. is grateful to the International Atomic Energy Agency for awarding him a fellowship. Note added in proo/~" Our attention was recently drawn to a paper by Ball and McGrory 39), in which they present calculated positions of all those levels in 9 1 N b and 93Tc that are of interest here. The agreement is very good except for the 2.5+ (v = 5) level in 93Tc. References 1) Iu. I. Kharitonov, L. K. Peker and L. A. Sliv, Phys. Lett. 31B (1970) 277 2) I. Bergstr6m, B. Fant, C. J. Herrlander, P. Thieberger, K. Wikstr6m and G. Astner, Phys. Lett. 32B (1970) 476 3) I. BergstrOm, B. Fant, A. Filevich, G. Lind6n, K.-G. Rensfelt, J. Sztarkier and K. Wikstr6m, Research Institute for Physics, Stockholm, annual report (1970) pp. 78, 96 4) J. M. Jaklevic, C. M. Lederer and J. M. Hollander, Phys. Lett. 29B (1969) 179 5) J. B. Ball, J. B. McGrory, R. L. Auble and K. H. Bhatt, Phys. Lett. 29B (1969) 182 6) J. Picard and G. Bassani, Nucl. Phys. A131 (1969) 636 7) R. L. Kozub and D. H. Youngblood, Phys. Rev. C4 (1971) 535 8) H. Ejiri, S. M. Ferguson, I. Halpern and R. Heffner, Phys. Lett. 29B (1969) 111 9) P. J. Riley, J. L. Horton, C. L. Holles, S. A. Zaidi, C. M. Jones and J. L. Ford, Phys. Rev. C4 (1971) 1864 10) M. S. Zisman and B. G. Harvey, Phys. Rev. C4 0971) 1809 11) C. M. Lederer, J. M. Hollander and I. Perlman, Table of isotopes, 6th ed. (Wiley, New York, 1967) 12) H. Ohnuma and J. L. Yntema, Phys. Rev. 176 (1968) 1416 13) K. T. Kn6pfle, M. Rogge, C. Mayer-B6ricke, J. Pedersen and D. Burch, Nucl. Phys. A159 (1970) 642 14) K. Hesse and E. Finckh, Nucl. Phys. A141 0970) 417 15) F. Rauch, Z. Phys. 243 (1971) 105 16) S. Matsuki, Y. Yoshida, M. Hyakutake, M. Matoba, S. Nakamura and I. Kumabe, Nucl. Phys. A174 (9171) 343 17) D. L. Mathews, T. P. Lindsey, M. Koike and C. F. Moore, Phys. Rev. C4 (1971) 1876 18) G. T. Garvey, W. J. Gerace, R. L. Jaffe, I. Talmi and I. Kelson, Rev. Mod. Phys. 41 (1969) S1 19) M. Grecescu, A. Nilsson and L. Harms-Ringdahl, Research Institute for Physics, Stockholm, annual report (1970) p. 12 20) A. Nilsson and M. Grecescu, Nucl. Phys. A212 (1973) 448 21) S. A. Hjorth, H. Ryde and B. Sk~.nberg, Ark. Fys. 38 (1968) 537 22) I. Bergstr6m, C. J. Herrlander, A. Kerek and A. Luukko, Nucl. Phys. A123 0969) 99 23) T. Yamazaki and G. T. Ewan, Nucl. Phys. A134 (1969) 81
HIGH-SPIN STATES (I) 24) 25) 26) 27) 28) 29) 30) 31) 32) 33) 34) 35) 36) 37) 38) 39)
447
C. M. Lederer, J. M. Jaklevic and J. M. Hollander, Nucl. Phys. A169 (1971) 449 T. Yamazaki, Nucl. Data A3 (1967) 1 L. Mesko, A. Nilsson, S. A. Hjorth, M. Brenner and O. Holmlund, Nucl. Phys. AI$1 (1972) 566 P. Thieberger and C. J. Herrlander, Research Institute for Physics, Stockholm, annual report (1968) p. 11 K. Abrahamsson, A. Filevich, K.-G. Rensfelt and J. Sztarkier, Nucl. Instr. 111 (1973) 125 L. Harms-Ringdahl and J. Sztarkier, Nucl. Instr. 108 (1973) 557 A. Luukko, A. Kerek, I. Rezanka and C. J. Herrlander, Nucl. Phys. A135 (1969) 49 N. Auerbach and I. Talmi, Nucl. Phys. 64 (1965) 458 A. de Shalit and I. Talmi, Nuclear shell theory (Academic Press, New York, 1963) pp. 409, 529 M. Goldhaber and A. W. Sunyar, in Alpha-, beta- and gamma-ray spectroscopy, ed. K. Siegbahn (North-Holland, Amsterdam, 1965) p. 931 R. S. I-[ager and E. C. Seltzer, Nucl. Data A4 (1968) 1 S. Cohen, R. D. Lawson, M. I-L Macfarlane and M. Soga, Phys. Lett. 10 (1964) 195 K. H. Bhatt and J. B. Ball, Nucl. Phys. 63 (1965) 286 J. Vervier, Nucl. Phys. 75 (1966) 17 V. I. Isakov, T. A. Kozhamkulov and V. I. Guman, Izv. Akad. Nauk SSSR (ser. fiz.) 36 (1972) 848 J. B. Ball and J. B. McGrory, Phys. Lett. 41B (1972) 581
Nuclear Physics A212 (1973) 429--447; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilmwithout written permission from the publisher
H I G H - S P I N S T A T E S I N T H E N = 50 I S O T O N E S 91Nb A N D 93Tc P O P U L A T E D I N (~,, p2nT) R E A C T I O N S M. GRECESCU t, A. NILSSON and L. I-[ARMS-RINGDAHL Research Institute for Physics, 104 05 Stockholm 50, Sweden Received 27 December 1972 Abstract: The reaction (ct, p2nT) on 9°Zr and 92M0 targets was used to populate excited states in 9tNb and 93Tc, respectively. The de-excitation of these states was studied by in-beam ),-ray spectroscopy. The ~,-ray transitions belonging to these nuclei were identified by studying coincidences with charged particles, excitation functions and )'-7 coincidences. Angular distribution and lifetime measurements were also performed. Many new levels were observed, particularly in 9aTe. They are interpreted in terms of shell-model calculations as belonging to the (g~r)3 and (P~r) (g~_)4proton configurations.
E
NUCLEAR REACTIONS 9°Zr, 92M0(~, p2n~,), E~ = 37--43 MeV; measured E~,, 1~, (Ec~, 0) tiT'-delay, pT-coin., ~,7-coin. 9lNb, 93Tc deduced levels, J, ~z. Enriched targets. Ge(Li) detectors.
1. Introduction D u r i n g recent years, several theoretical and experimental investigations have been devoted to the properties o f multi-particle states belonging to a multiplet configuration ( j ' ) or to the associated configurations {(jn),jl = ½}. K h a r i t o n o v et al. 1) have pointed out the correlation between the level structure o f these configurations and the properties o f residual nuclear interactions. The experimental studies have been confined mainly to p r o t o n multi-particle states in nuclei with a magic n u m b e r o f neutrons. E.g., in the region of N = 126, Bergstr6m and co-workers 2,3) have studied the following configurations: (~zh~)2 in 21 Opo ' (nh~_)3 in211At and (nh~)3 (vp~r)-i in 21 OAt . In the region o f N = 50, the (r~g~) 2, {(ng~)3(np½)} and (Trgl) 4 configurations in 92M0 and 94Ru, respectively, have been studied both experimentally and theoretically 4, 5, 24). In the same region it would be interesting to establish experimentally the level structure o f the (~g~)3 configuration which can provide information about the parameters o f central and tensor residual interactions 1). The (ng~)a configuration can be f o u n d in 43Tcs 93 o- The g r o u n d state o f this nucleus m a y be regarded as consisting o f the {(7~p~)2(rcg~) a} configuration outside an inert t Present address: Institute for Atomic Physics, Bucharest, Romania. 429 October 1973
430
M. GRECESCU et
aL
aS~Srso core s). It is reasonable to expect among its excited states a number of seniority-three states due to the three g~ protons. The highest spin obtainable in this way is 21_. Negative-parity states are also expected in 93Tc due to the promotion of one p~ proton to the g~ orbital. Up to the beginning of the present investigation, the experimental knowledge of the level structure of 93Tc was confined to low-spin states of single-particle type populated in (3He, d) reactions 6, 7) or in the decay of isobaric analogue states a). Recently, studies have also been made by means of (d, n) reactions 9) and (ct, t) reactions 1o). The lowest excited state is a ½- isomeric state at 393 keV with a halflife of 44 rain [ref. 11)]. The population of 93Tc levels in the radioactive decay of 93Ru (T~ = 63 s) was virtually unknown. The level structure of 91Nb has been investigated by stripping and pick-up reactions 6, 12, ~3), by the radioactive decay of 91Mo and 91raMo [ref. 14)], and by the (P, 7) reaction is). It has also recently been studied by means of the (p, nT) reaction ~6, ~7). The lowest excited state is a ½- isomeric state at 104.5 keV with a halflife of 62 d. The (~zgl_)3configuration should appear also among the excited states of ~lNb5 o by raising the p½ proton pair to the g~ orbital. The previous considerations prompted us to start an investigation of high-spin states in 93Tc and 91Nb, populated preferentially by nuclear reactions with eparticles. A preliminary report of this work has been published previously 19).
2. Experimental procedure 2.1. TARGETS AND REACTIONS The excited states of 9aTc and 91Nb were obtained via the (0t, p2n~) reaction on
92Mo and 9°Zr isotopes. The Mo target consisted of 10 mg Mo powder, enriched to 98.3 7o in 92Mo; the Zr target consisted of 13 mg ZrO 2 powder enriched to 97.6 in 9°Zr. The targets were prepared by depositing the powder between two Formvar foils of 150 mg[cm 2 each. The mean target thickness was 10-20 mg/cm 2. The (~, p2n) reaction occurred simultaneously with the (~, 3n) reaction when bombarding the targets with an ~t-particle beam having an energy between 37 and 43 MeV. The strong competitiveness of the (~, p2n) compared to the (~, 3n) reaction is due to the low binding energy is) of the proton compared to that of the neutron in the considered region of neutron-deficient nuclei. For example, in the case of the 92Mo target, the Q-value of the (~, 3n) reaction is -33.02 MeV whilst that of the (cq p2n) reaction is -26.06 MeV and the Coulomb barrier for the proton is about 7 MeV. The results concerning the nuclei produced by (~, 3n) reactions on 9°Zr and 92Mo are presented in an accompanying paper 20). The s-particle beam with a maximal energy of 43 MeV was delivered by a fixed frequency cyclotron with a 225 cm pole diameter. The energy was lowered stepwise by introducing degrading foils at a focal point in the beam transport system.
HIGH-SPIN STATES (I)
431
The geometry of the experimental arrangement is described in previous publications 21,22) from this laboratory. 2.2. ENERGY, INTENSITY AND A N G U L A R DISTRIBUTION MEASUREMENTS
The y-radiations were detected with a 40 cm a coaxial Ge(Li) detector ( F W H M 2.5 keV at 1173 keV) and a 5 mm thick planar Ge(Li) detector for X-rays ( F W H M 650 eV at 122 keV). For the study of excitation functions, the detectors were placed at an angle of 126 ° with respect to the beam direction, in order to reduce a possible anisotropy effect (P2 (cos 126 °) = 0). The spectra were recorded on a 4096-channel Intertechnique pulse-height analyser and they were subsequently computer-processed, in order to determine the positions and areas of the photopeaks. The energy and intensity calibrations of the spectrometer were performed off-beam with a set of radioactive standard sources provided by the IAEA. An in-beam check on the energy calibration was provided by several strong activity lines occurring especially in the irradiation of the 92Mo target. The agreement between our energy values for these lines and recent data from radioactive decay studies is generally within 0.2 keV. We assume that for strong and well resolved lines the errors in the energy and intensity values are less than 0.3 keV and 10 ~ , respectively. A few of the observed y-rays were common to all spectra: 110, 184, 197, 238, 597, 690 and 937 keV; they are due to a-particle reactions on 160 in the targets and to neutron interactions in the Ge(Li) detector 2a). The angular distributions of y-rays relative to the incident beam direction were measured at five angles between 90 ° and 155 °. The normalization of the experimental data was performed by monitoring the beam intensity with two surface-barrier Si detectors mounted symmetrically relative to the beam axis, at angles of + 25 °, in the horizontal plane. The sum of the counts delivered by the two detectors was corrected for the dead time of the multichannel analyser, and was taken as a measure of the total charge incident on the target during the live-time. The normalization procedure was checked with the angular distributions of two known isomeric transitions 24) appearing in the spectra: 148 keV (T½ = 220 as) in 92Mo and 145 keV (T, = 73/~s) in 94Ru; in both cases we obtained the expected isotropic distribution. The experimental angular distributions were fitted by a least-squares analysis to the expression:
W(O)=
coast [1 + A~xPP2(cos 0) + A~,Xr'P4(cos0)].
(1)
In order to convert the experimental values A~,xp to the corresponding theoretical coefficients for complete alignment A~ ax, tabulated by Yamazaki 25), the attenuation coefficients O~k(Ji) = .cakAexplAmax/rlk
(k = 2, 4)
must be known. Unfortunately, in the case of our targets only two ~2 coefficients
432
M. GRECESCU et al.
could be experimentally determined from known pure El and pure E2 transitions without delayed (T½ > 10 ns) components (126 and 1033 keV in 94Ru). Since, however, these values agreed with the attenuation coefficients previously obtained for 95Mo and 97Mo [ref. 26)], we used the latter in the interpretation of our angular distributions. The interpretation was perfolmed along the same lines as described in the appendix of ref. 26). 2.3. LIFETIME MEASUREMENTS The half-lives of delayed y-ray transitions were measured with the experimental facilities described in refs. 27,28). The lower limit of measurable half-lives was determined mainly by the time resolution of the system and was about 10 ns. The upper limit in the ns region was determined by the time interval between successive beam pulses. This interval was normally 125 ns but it could be increased up to 625 ns by using an electrostatic beam deflecting system. For longer half-lives, a magnetic beam pulsing was employed, covering a range from about 10 #s up to a few seconds. A gap existed for half-lives in the decade 1-10 #s, where no accurate measurements could be performed with the available systems. The adopted measuring procedure consisted in taking two-dimensional spectra with 512 energy channels and 8 time channels. The energy region of interest was covered in two steps: 100-900 keV and 900 keV-2 MeV. 2.4. COINCIDENCE MEASUREMENTS 2.4.1. The y-y coincidence measurements were performed with a computer online system 29). Two 40 cm a Ge(Li) detectors were placed in the horizontal plane at angles of about + 135 ° relative to the beam direction and mutually screened. The coincidence system was of the conventional fast-slow type, having a resolving time of about 80 ns, thus eliminating any influence from neighbouring beam pulses with a time distance of 125 ns. The beam intensity was adjusted in order not to deteriorate the resolution of the energy spectra due to high singles counting rate. The true/random coincidence ratio was then well above 10, and the coincidence rate about 200 coinc./s. Each detector was coupled to a 4096-channel ADC. The digital information about each coincidence event was transmitted to the computer and stored on magnetic tape, The main analysis of the data was performed off-line by reading the tapes into the computer memory. By setting gates in the spectrum from one of the detectors, the corresponding coincident spectra from the other detector could be singled out. A maximum number of 32 gates could be set simultaneously. 2.4.2. In order to separate the y-ray transitions belonging to the (~, p2ny) reactions, p-~ coincidences were measured at E~ = 43 MeV. The proton detector was a Si surface-barrier detector with ~ = 5 mm and a depletion depth of 2 ram, placed at about 135 ° with respect to the beam direction. The output of the fast-slow coin-
433
HIGH-SPIN STATES (I)
cidence system was gating the multichannel analyser recording the ),-ray spectrum. Because of the crucial importance of these measurements for the isotopic assignment of ~,-rays, the correct operation of the system was carefully tested. The energy spectra of charged particles emitted by the target were measured for enriched H2Sn and 1248n targets, In the neutron-rich 12¢Sn only (g, xn) reactions occur and the charged particle spectrum corresponds to the g-particles scattered in the target. No elastically scattered g-particles were observed. In the neutron-deficient 112Srt the (g, xn) reactions were known to compete with~ the [g, p ( x - 1)n] reactions a0) and a charged particle spectrum with energies between 3 and 14 MeV and with a typical evaporation shape was obtained. Another test was provided by the ),-ray transitions due to g-particle reactions on 60 (see table 1). Only the lines belonging to (g, p) and (g, pn) reactions were seen in the p-~, coincidence spectra. TABLE 1 Gamma-ray transitions produced by 43 MeV m-particle reactions on x60 in a 9°ZrOz target Energy (keV)
110 197 184 937 238
Reaction
160(g, 160(g, 160(ct, 160(g, 160(g,
p)lgF p)19F pn)laF pn)laF n)t 9Ne
T1. (ns)
I (arb. units) in the singles spectrum
prompt 88 150 150 18
6.8 36 124 151 22
I (arb. units) in the proton coinc, spectrum meas. calc. a) 6.8 8.0 19.6 21.3 0
5.3 8.5 18.5 22.5 0
a) The calculated values (arbitrarily normalized) take into account the time resolution (2r = 90 ns) of the coincidence unit.
The chance coincidence rate was low, so that the y-rays belonging to (g, 2n) reactions in the targets are missing in the proton-coincidence spectra, though they were quite strong in the singles spectra. Since the Si detector was sensitive also to g-particles, the y-transitions in 9 t M o , 199.5, 211.7, 653.8, and 1413.9 keV [ref. 2o)], were found in the coincidence spectrum of the 9 2 M o target, being excited by the 9 2 M o ( g , g'n)~)91Mo reaction. These y-rays were missing in the proton coincidence spectrum of the 9ozr target ' since in that case they were excited by the 9°Zr(g, 3nT)91Mo reaction. 3. Experimental results
A typical spectrum obtained from the 92Mo target at E~ = 43 MeV is represented in fig. 1. It contains about 140 y-ray lines, 25 of them having half-lives > 1 m. The residual y-ray activity of the target has been investigated and the corresponding radioactive nuclei were identified. Their presence shows that at least eight different
"10~!
i
'°I
s3H o
g 7~tSSRu;
F~aX-rays
I
2,oo
~
I
S3Mo
~ ~3~
J
~
~*
~s'oo
i
soo
511
II
m~
CHANNEL
,doo
,o'oo NUMBER
~
I
~Ho
9~H°
3~'oo
18F
,~o
;
2doo
~- particles
,o'oo
Fig. 1. The y-ray spectrum recorded by a 43 cm a Ge(Li) detector at 0 = 126 ° during bombardment of 92Mo with 43 M e V co-particles. T h e lines for which energies, but not nucleide assignment, are given should belong to 93Tc (or possibly 93Ru). A n asterisk indicates lines ascribed to 93Ru.
435
HIGH-SPIN STATES (I) TABLE2 Residual activity of a 92Mo target bombarded with 43 MeV ~-particles Radioactive nucleus
T~
Origin
9°Nb 9°Mo 91raMo 93mMo
14.6 h 5.7 h 66 s 7 h
Decay of 9°Mo (~, ~'2n) (~, ~'n) (¢~,2pn)
9aTe 93mTc 93Ru 94Tc
2.8 44 65 5
94mTc 94Ru 95Tc 95Ru
52 rain 53 min 20 h 1.65 h
h min s h
(e, p2n) and decay of 93Ru (~, p2n) (~, 3n) (c¢,pn) Decay of 9'~Ru (g, 2n) Decay of 95Ru (~, n)
Comments
Not populated in the decay of 93mTc and 9aTe
Not populated in the decay of 94Ru Probably also (~, pn)
reactions occur in the target (see table 2). The relative yields of the (e, 3n), (~, p2n), and (e, 2pn) reactions at 43 MeV are 1 : 11 : 12, as estimated from the intensity of the -~+ -+ $+ transitions in 93Ru, 93Tc, and 93mMo. A picture of similar complexity is found also for the 9°Zr target (about 110 v-ray lines in the spectrum obtained at E~ = 43 MeV). In this case, the relative yield of the (e, 3n) and (~, p2n) reactions is 4 : 1, as judged from the _13+ _~ $+ transitions. The assignment of v-ray transitions as belonging to the (e, p2n) reaction, is based on the following arguments: (a) Shape of the excitation function; in the energy range E~ = 3 7 - 4 3 MeV the excitation functions of the reactions (e, xnyp) with x + y --- 3 are increasing with respect to those of the (e, 2n) reaction. (b) Coincidences with charged particles (see subsect. 2.4.2). (c) Coincidences with v-ray transitions which in turn are coincident with charged particles. This is the case for a few lines which were not observed directly in coincidence with charged particles due to poor statistics. The construction of level schemes for 93Tc and 9 t N b and the spin-parity assignments are based on the following experimental information: V-V coincidences and relative intensities in the coincidence spectra; lifetime measurements; relative shape of the excitation functions; angular distribution data. Besides its use for the isotope assignment, the eXcitation function of a transition can also give valuable indications about the spin of the emitting level. It has to be used quite carefully, however, since at high e-energies it is expected to be rather insensitive in the range of low spin values [cf. fig. 5b in the following paper 2o)], and since weak lines belonging to the next higher isotope may appear in unresolved doublets and make the spin appear too low [cf. the 284.5 keV line in fig. 2 of the following paper].
436
M. GRECESCU et al.
3.1. THE NUCLEUS 93Tc The ~-ray transitions assigned to 93Tc are listed in table 3. The excitation functions for the strongest transitions are represented in fig. 2. The results o f the ~,-y coincidence measurements are summarized in table 4. TABLE3 Gamma-ray transitions from the reaction 92Mo(~t, p2ny)93Tc at E~ = 43 MeV E~, ") I~, Isomeric b) (keV) relative fraction (%) 350.3 523.2 607.5 629.3 680.5 711.0 750.4 1095.9 1434.2 1515.8 1721.9
33 5 28 15 7 28 58 38 100 24 8
2 0 10 72 10c) 73 22 0 40 67 0
Angular distribution A2~ '
0.254-0.01 0.404-0.04 0.294-0.03 --0.154-0.02 --0.474-0.08 0.10-4-0.02 0.124-0.01 0.264-0.02 0.174-0.02 --0.154-0.03 0.404-0.04
Assignment
A.~' --0.084-0.02 --0.084-0.08 --0.094-0.05 0.004-0.03 0.054-0.10 0.004-0.03 --0.074-0.02 --0.104-0.03 --0.024-0.04 +0.114-0.04 --0.064-0.08
2535(-2]L+) -+ 2185(3~-+) 3918(~--) --* 3311(-~-) 2145(-~--) ~ 1516(-~L+) 680(7+) ~ g.s.(9+) 2145(~L-) -+ 1434(-~ +) 2185(3~-+) --* 1434(~- +) 3311(~--) --* 2215(~Z-) 1434(-~- +) ~ g.s.(9+) 1516(.~- +) --> g.s.(9+) 4257(-2~+) --~ 2535(~L +)
Coincident with charged particles yes
yes yes yes (weak) yes yes (weak) yes yes
yes yes (weak) Coincident with 350.3 keV
y-ray transitions tentatively assigned to 9aTc
70.0 707.8 781.2 788.8 835.9
2 2 1 2 1
2215(~Z-) ~ 2145(~--) 2223(~ +) --~ 1516(3~-+) 2215(~--) -~ 1434(~- +) 2223(-~ +) ~ 1434(~- +) 1516(~-+)~ 680(½+)
--0.114-0.08
a) 4-0.3 keV. b) The isomeric parts have 1 /~s < T~. < 10/ts except for the 680.5 keV y-ray. c) 65 s activity populated in the decay of 93Ru. Since m a n y transitions have a p r o m p t and a delayed c o m p o n e n t in the/as range, the values o f the angular distribution coefficients were c o m p u t e d f r o m the data in table 3 with the relation (Aexp~ Zak /prompt ~
exp
ak Iy/I~prompt.
The proposed level scheme is presented in fig. 3. The spin-parity assignments o f the g r o u n d state and o f the first excited state are ~+ and ½-, respectively, according to previous experiments 6).
437
HIGH-SPIN STATES (I) TABLE 4
F-7 coincidences observed in 9aTe Coincidence gate (keY)
350.3 607.5 629.3 711.0 750.4 1095.9 1434.2 1515.8 1721.9
Coincident ?-rays (keV) 350.3
523.2
607.5
629.3
711.0
750.4
yes
1095.9 1434.2 1515.8 1721.9
yes
yes
yes
yes weak
weak yes yes
yes
yes
yes yes weak yes
yes
yes
yes
I¥(E)
100 80 6o
100
\
E¥(keV) 1434.2
13/2~912"
750. ,'.
17/2~13/2"
\\
"-~x \ I \.\ \
/,0 •
"
"
"
20 "------~ lO
,~+
8 6
l r~.{,........~,,~ ~.~,)/+/~'
z,
j+
2
3503 711.0 607.5 1515.8 756.1
2112"-~47/2" 13/2~13/2 ° (25/27~.21/2-) 11/2"-~. 9•2" 4"~2+ (a.,2n)
629.3
13/2~11/2+
1721.9 6805
2512t~21/2" ( 7 / 2 ~ 9/2"
523.2
70.0 707.8
~
(17/2-~-13/2") (15/2"--~11/2*)
f 1
37
39
,',1
43
Eet(MeV)
Fig. 2. Excitation functions of y-rays assigned to 93Tc.
The 680 keV level Since the 680.5 keV ~-ray is the only one accompanying the decay of 9 3 R u [ref. 2o)], it may be assumed to be a transition to the ground state. The character of the angular distribution suggests a IAJI = 1 transition, implying spin values of 5 + or J~-+ for the 680 keV level. These values are also supported by the logft value of 6.5 for the branch of the 9 3 R u decay that feeds the 680 keV level (assuming that the ground state of 9 3 R u is ~ + ) . A }+ assignment would be in good agreement with theoretical predictions 31, 37).
438
M. GRECESCU
25/2"
4257
(25/2")-- I
3918
,2,,I _
et al.
( .....
----
m
3311
2535 2223 2215 (1p.s.~Tl12.40ps) 2185 2145
(
1516 1434
680 393
93
43Tc50
]Fig. 3. Proposed level scheme for 93Tc.
From the angular distribution data, a mixing ratio 6 ( E 2 / M 1 ) = 0.7+0.2 is obtained for the 680.5 transition, suggesting a great MI hindrance. This is to be expected if the 5 + level belongs to the (g~)3 multiplet, as the M1 transitions between the members o f a (j)" multiplet are forbidden 32). "[he 680 keV level was also weakly excited in the reaction 92Mo(3He, d)93Tc [E = 660+20 keV, ref. 6)], in 92Mo(~, t)93Tc [E = 680+20 keV, ref. to)], and in 92Mo(p, y)93Tc [E = 680+ 10 keV, ref. s)], probably due to a ng~ admixture in its wave function 1o). The levels at 1434, 2185, and 2535 keV. The strongest y-ray transition in 93Tc is 1434.2 keV, which can feed only the ground state. The coincidence measurements indicate the existence of a cascade 350.3 keV ~ 750.4 keV ~ 1434.2 keV. The order of the transitions in the cascade is established by the relative intensities in the singles spectra and in the coincidence spectra. The angular distribution data (A2 > 0, A, < 0) are consistent with AJ = - 2 for all three transitions and this fact, together with their prompt character (T, < 10 ns), indicates that 350.3 keV and 750.4 keV are E2 transitions and that 1434.2 keV is quite probably also E2. The following assignments are proposed: 1434 keV (_13_+), 2185 keY (17 +) and 2535 keV (-~-+).
HIGH-SPIN STATES (I)
439
The 4257 k e V level. The 1721.9 keV line is coincident with the 350.3 keV y-ray and precedes it, according to the relative intensities in the singles and coincidence spectra. Its angular distribution indicates that A J = - 2 , and the existence of a Doppler tail that it cannot be an M2 transition [the flight time of the recoiling nuclei is estimated to be less than 1 ps, ref. 20)]. The excitation function is typical for a high-spin state, leading to a spin-parity assignment of ~ + for the 4257 keV level. The 1516 k e V and 2145 k e V levels. The 1434.2 keV line is also coincident with a 711.0 keV line, suggesting the existence of a level at 2145 keV. Another cascade observed in the coincidence measurements, viz. 629.3 keV ~ 1515.8 keV, is obviously de-exciting the same 2145 keV level (within 0.I keV). The relative intensities show that 1516 keV is the ground state transition, originating in a level with the same energy. The angular distribution data clearly favour ~1_+ for this level, the M1 part of the de-excitation being strongly hindered. A weak 835.9 keV line observed in the spectrum is presumably the _11_+ ~ ~2+ transition. The angular distribution of the 629.3 keV transition (A2 < 0) and the absence of a ground state transition suggest the assignment _13 for the spin of the 2145 keV level. This value is also corroborated by the angular distribution of the 711.0 keV line (A2 > 0, A4 ~ 0) which is consistent with a fairly pure dipole transition between two states of the same spin. The non-observation of a direct -13 ~ $+ transition with an energy of 2145.2 keV (relative intensity < 0.5 ~o with respect to 1434.2 keV) proves that this is not an E2 transition and consequently, that the 2145 keV level has spin-parity 1.~-. The absence of the 2145.2 keV M2 transition implies a fully reasonable M2 hindrance 33). The 2215 k e V level. Each y-ray transition belonging to the cascades originating from the .13_- and -~-+ levels contains a delayed component with 1 #s < T~ < 10 #s: We assume that the half-lives are identical and that the -~-- and 1-x7-+ states are fed from the same isomeric state. The absence of a transition from this state to the ~- + level, as well as the observed half-life, suggest a tentative spin-parity assignment of _~_7-z for the isomeric state. A careful examination of the low-energy part of the spectrum (between 30 and 100 keV) with a Ge(Li) X-ray detector leaves as the only possible candidate for the higher-energy isomeric transition a 70.0 keV line. Its excitation function is in agreement with the spin assignment, and the angular distribution is isotropic. Unfortunately, its half-life could not be measured because of the limitations of the measuring system at low energies. Another weak point is the existence of an unbalance by a factor of 3 between the intensity sum of the delayed components of the 629.3 keV and 711.0 keV transitions and the intensity of the 70.0 keV transition corrected for internal conversion [~Xtot = 5.16, ref. 34)]. This unbalance may partly be explained by possible errors in the detector efficiency calibration at low energies, and by the rough estimate of the delayed/prompt ratio in the time measurements. The energy of a weak 781.2 keV line fits within 0.2 keV with a possible M2 transition between the 2215 keV isomeric state and the -~-+ state at 1434 keV. The Weiss-
440
M. GRECESCU et aL
kopf estimate for half-lives gives 2.4 #s (corrected for internal conversion) for a 70.0 keV E2 transition, and half-lives also in the/ts range for 30.6 keV E1 and 781.2 keV M2 transitions, assuming reasonable retardations. In conclusion, we assume that the isomeric state at 2215 keV has a spin-parity of ~ -. The 2223 k e V level. The existence of a 12--s-+state in this energy region is suggested by the theoretical calculations 23) and seems to be supported by the observation o f two weak y-rays at 707.8 keV and 788.8 keV. The sum-energy relations 707.8 + 1515.8 = 2223.6 keV and 788.8+ 1434.2 = 2223.0 keV are in agreement with the expected de-excitation of the 12-Aslevel via the -~+ and -y-+ levels. The fact that the two lines have about the same intensity indicates a high M1 hindrance. Their excitation functions are consistent with the spin assignment but their low intensity prevented their placement to be checked by use of the coincidence spectra. The levels at 3311 k e V a n d 3 9 1 8 keV. A strong cascade observed in the coincidence measurements is 607.5 keV ~ 1095.9 keV. It is almost certainly a stretched E2 cascade, according to the prompt character of the lines and to their angular distributions. The cascade cannot terminate at the ground state because the excitation functions require much higher spins than )~- and ~ for the levels involved. On the other hand, the terminating state must be long-lived, since we do not see any additional coincidences. The most reasonable conclusion then is that the cascade feeds the ~ isomeric state. The excitation functions are in agreement with ~ - and ~s.- assignments for the 3311 keV and 3918 keV levels, respectively. The strong population of the isomeric state is also explained in this way and the side-feedings of the ~7_+ and ~7 - states become similar in strength. A direct confirmation of the placement of the cascade in the decay scheme would require rather delicate delayed coincidence measurements. A 523.2 keV y-ray was seen in coincidence with the 350.3 keV transition. Its excitation function indicates a high spin for the initial state and the angular distribution and lifetime suggest an E2 character. However, the transition was not included in the level scheme because the coincidence measurements did not exclude its placement on top of the 1721.9 keV transition. 3.2. THE NUCLEUS 91Nb The y-ray transitions assigned to 91Nb are listed in table 5. The excitation functions are presented in fig. 4. Because of the relatively low cross section of the reaction 9°Zr(0c, p2ny)91Nb, only six lines are unambiguously assigned to 91Nb. The coincidence measurements show that three of them form a cascade 356.7 keV --* 819.3 keV ~ 2291.1 keV, the order being established by their relative intensities. The angular distributions and the prompt character of these lines indicate that the cascade consists of stretched E2 transitions. The following spin-parity assignments are proposed, supported by the excitation functions: 2291 keV (_x3+), 3110 keV (-~-+), 3467 keV (2--1-+). A level at 2292 keV which is probably identical with our 2291 keV level was observed in the reaction 91Zr(p, ny)91Nb [ref. 16)].
HIGH-SPIN
441
STATES (I)
TABLE5 Gamma-ray transitions from the reaction gOZr(a, p2ny)g1Nb at E, = 43 MeV
E, ‘7 (kev)
1-l
Half-life “)
Assignment
Angular distribution
relative A,‘“P
193.8
65
16 % prompt
A.$==p
0.05&0.02
0
Coincident with charged particles
1984
+ 1790
yes
3467(?-+)
+ 3110(-1_i+)
3110(7+)
+ 2991(?+)
yes yes
1790
+ g.s.(9+) 2
+s4 % (T+ = 120 ns) 356.9
61 ‘)
519.4
98
96 % prompt
1790.4
69
30 % prompt
prompt
0.29 *0.02 d,
-0.10*0.03
0.31*0.02
-0.10~0.03
d)
+4 % long
1984.3
97
0.08&0.03
0.03 10.04
Coincident
+70%
with
(T+ = 120 ns) 30 % prompt
193.8 keV 0.05
i-o.04
0
1984
--f g.s.(F+) 2
2291(=+) 2
-+ g.s.(T+) 2
+70% (T+ x 120 ns) 2290.7
100
87 % prompt
0.21 *to.03
-0.09+0.05
Coincident with
+I3 % long
819.4 keV “) “) ‘) ‘INb d,
&0.3 keV. “Prompt” means T+ < 10 ns and “long” means T+ > 200 ns. The 356.9 keV peak is actually an unresolved doublet; the intensity of the contribution was estimated from coincidence measurements. For the unresolved doublet.
IyE)
Ey keV
Iy(2290.7)-loo LOO -
.-_-_.__------__* *\ \
200 -
.
16139
\
‘\\
,oo - 2%
21964.3 %2
*\ 80 -
\ .
60 - ._.,.i,:
. LO37
39
41
'W 356.9 15095
43 E,.MeV
Fig. 4. Excitation functions of y-rays assigned to 9’Nb.
from
442
M. GRECESCU et al.
21/2"
21/2"
3.70
17/2"
3.32
3~67
17/"2"
3110
13/2+
2291
1984
11/2-,
2.62
1~
2.46
1~2-
2.18
9/2-
192
9/~
0
1790
9/2+H
0
EXPERIMENTAL
CALCULATED
91Nb ,'.1 S0 Fig. 5. Proposed level scheme for 91Nb. The assignments for the negative-parity states are taken from ref. 1s), and the calculated levels which are relevant to the comparison with experimental data are taken from ref. al).
According to the coincidence measurements, another cascade is formed by the 193.8 and 1790.4 keV ~-rays. The cross-over transition 1984.3 keV is also present. The corresponding levels at 1790 and 1984 keV have been observed also in refs. 15, ~~). With our experimental data we were not able to check the spin-parity assignments proposed for these levels in ref. 15). The proposed level scheme for 91Nb is presented in fig. 5. 4. Discussion
Shell-model calculations of 9 t N b and 93Tc energy levels have been performed by several authors a 1, a 5-37) with the following assumptions: (i) only proton-proton interactions in the p½ and g~ 0rbitals are important; (ii) the seniority is a good quantum number in these orbits. Cohen et aL as) proved that the last assumption was almost exactly fulfilled, by calculating the seniority admixtures in the wave functions of several nuclei with N = 50.
HIGH-SPIN STATES (I)
443
"lhe results obtained by different authors are rather similar. We shall follow the calculations of Auerbach and Talmi 31), which are closer to the experimental results. Unfortunately, their calculations are based on obsolete experimental data for the nuclei around 90Zr" For example, the adopted energy values for the excited states of 92Mo, which play an important role in the calculations, exceed the presently known values by 30-50 keV. These differences are obviously reflected in the values of the residual interaction matrix elements. For both 91Nb and 93Tc, the 50 neutrons and the first 38 protons are included in 88 an inert core (3sSrso). The low-lying positive-parity states in 93Tc are due to the (p~)Z(g~)3 proton configuration. It contains the spin sequence from ~+ up to 2~_+, with the exception of a-~+ which is excluded by the Pauli principle. All of the levels belonging to this band were experimentally observed by us, with the exception of three low-spin states (½+, ~-+ and ~+ (v = 3)). There is full agreement between the calculated level order and the experimental results. The calculated energies are slightly higher than the experimental ones. It is interesting to observe that a linear relationship exists between the calculated and the experimental level energies. The relation obtained by a leastsquares fit is: E(fitted) = 69+0.892 E(calc.)A.T"
(E in keV).
It gives an r.m.s, deviation of only 7 keV with respect to the experimental values. The fact that the slope of the line is smaller than 1 can be formally interpreted as a weakening of the interaction when a proton is added to the (g~_)2 configuration. A linear relationship with the same r.m.s, deviation was also found between our experimental data and the levels calculated by Vervier 37), but the agreement is poorer: E(fitted) = 230+0.787 E(calc.)v
(E in keV).
The observed 2s+ level can be interpreted as the highest-spin state obtainable in the (g~)5 configuration. The seniority-five states of this configuration are obtained by raising the p½ proton pair to the g~ orbital and decoupling it. This operation should require an energy of about 2 MeV, judging from the position of the first 2 + state in 9°Zr. This estimate is in good agreement with the observed difference between the 2s_+ state and the highest levels belonging to the (p~.)2(g~_)3 configuration. Among the (g~)5 levels only the 2__5_+level was observed; this is probably due to the fact that it is the only one close to the "yrast" line. All the other levels are probably situated much higher than those having the same spin but belonging to the (gl)3 configuration. The strong cascade observed in the positive-parity band of 93Tc (2_~+ ~ 21_+ 1_~_+ ~ _123+ _~ ~2+) is typical of a de-excitation cascade involving yrast levels. The negative-parity states in 93Tc are due to the (p~)(g~)4 configuration. According to Auerbach and Talmi [ref. 31), eq. (14)] the total energy of a state belonging
444
M. G R E C E S C U et al.
to this configuration is given by the relation:
[flJo E = Cp+4C,+V(g~Jo)+4c~ + [ - / ~ ( J o + l )
for for
J = Jo+½ J = Jo-{,
(2)
where C O = single proton energy in the 2p} orbit; Cg = single proton energy in the lg~_ orbit; V ( g ~ J o ) = (g~Jol Vpplg~Jo> matrix element of the proton-proton interaction in a state with definite spin Jo; ~ = average interaction between the p} proton and the g} proton; ]Y = splitting parameter. As there are no published results about the negative-parity high-spin states in 93Tc, we performed the necessary calculations. /..72
MeV
~58 L5 /.257
25/2 +
3919
(25/2-)-- - - - - - - /
3311
(21/2-)-- - - - -
/
&O
/
2112"
3.87
3.5
2535 2223 27..15 2185 21/,5
1516 1/,34
-
-
15/2"
317
-
-
1112"
2.97
21/2* 17/2" 7/2"
2.76 2.80 2.57
17/2+ 9/2"
2.38 2.26
9/2 +
1.9/,
9/2 + 312-
1.73 1.71
13/2+
1.53
5/2 +
1.33
21/2 + (15/2.)~ ( 1 7 / 2 " 17/2+ - - . - - / / 13/2- ~ "
11/2 + • 13/2 +
)
~
/ /
3.0
20
1.5
1.0
680
7/2 ÷
7/2 +
0.69
393
1/2" ~
1/2-
0.41
9/2*
~
EXPERIMENTAL
O.5
9/2+
CALCULATED
93
~3Tc5o
Fig. 6. Comparison between the proposed level scheme for 93Tc and the results of theoretical calculations. The calculated energies of the positive-parity levels were taken from ref. a,).
HIGH-SPIN STATES (I)
445
The seniority-four matrix elements V(g~Jo) were computed from the V(g~J') valuest given in ref. 31) with the relation: (J"~Jol ~ V~klJ"OtJo> = ½n(n--1) ~. [jn-2(0~ 2 J2)j2(j')Jol}J"~Jo]2(j2J'[Vpp]j2j'>, ~<~ ,2s2s" (3) where
[y-2( 2s2)j (s')Sol}Y :o] are the two-particle c.f.p. [ref. 32)]. The numerical values of the other parameters were also taken from ref. ax). The results of the calculations are presented in fig. 6 together with the positiveparity states and the experimental level scheme. The highest spin obtainable is _~z- for the seniority-three states and ~ - for the seniority-five states tt. In each doublet with J = Jo +½ and J = J o - ½ , the high-spin state has the lowest energy. The level order of the negative-parity states is in agreement with the proposed assignments but the calculated energies are too high. In particular, the 1_~- state should lie about 200 keV lower in order to give to the observed isomeric state. This is quite reasonable because the numerical values of the parameters employed in the calculations are average values for nuclei around 9 ° Z r and r.m.s, deviations of about 100 keV were observed 23). The strong population of the negative-parity band can be explained by the fact that the highest-spin state from the band ( ~ - ) is slightly lower than the -~+ state and thus represents an yrast level. The ground state of 91Nb is mainly due to the proton configuration (p~)2g~ and the positive-parity excited states are due to the (~zg~)a configuration. The excited states are obtained by raising t h e (p½)2 proton pair to the g~ orbital and decoupling it, which explains the big energy gap between the ground state and the positive-parity excited states. The relevant calculated levels are represented in fig. 4 together with the proposed level scheme. Also in this case, a linear relationship was established between the calculated al) and the experimental level energies: E(fitted) = 44 + 0.949 E(calC)A.T"
(E in keV).
Quite recently, the preliminary results of this investigation 19) have been used in theoretical calculations of the positive-parity states in 91Nb and 9aTe [ref. as)]. The main conclusion is that the seniority-three states belonging to the (zrgi) a configuration are fairly pure. 5. Conclusions
Several previously unknown excited states in 9XNb and 93Tc were populated by (~, p2n?) reactions at 43 MeV or-particle energy. Spin-parity assignments were proposed for most of these levels. Many of them are high-spin states (up to ~ - ) t There is a printing error in ref. 31): thus V(gl2 J ' = 8) should be --0.69 MeV. t* We define the seniority of a state belonging to a mixed-shell configuration (jlnO (j2 n2) of identical nucleons as the sum of the seniorities of the various equivalent groups.
446
M. GRECESCU et al.
belonging to the yrast levels. A comparison of the experimental data with theoretical calculations based on the shell model in the seniority scheme confirms that this model correctly describes the level schemes of N = 50 nuclei. Most of the newly discovered levels belong to the (zcg~_)3 or to the (lrp~)(~rg~)4 configuration; they provide a useful experimental basis for more detailed investigations of proton-proton interactions in the 2P½ and lg~: orbitals. The authors acknowledge the cooperation of the 225 cm cyclotron staff during the experiments. One of us (M.G.) wants to express his thanks to Prof. I. Bergstr6m for the possibility of working at the Research Institute for Physics, Stockholm. M.G. is grateful to the International Atomic Energy Agency for awarding him a fellowship. Note added in proo/~" Our attention was recently drawn to a paper by Ball and McGrory 39), in which they present calculated positions of all those levels in 9 1 N b and 93Tc that are of interest here. The agreement is very good except for the 2.5+ (v = 5) level in 93Tc. References 1) Iu. I. Kharitonov, L. K. Peker and L. A. Sliv, Phys. Lett. 31B (1970) 277 2) I. Bergstr6m, B. Fant, C. J. Herrlander, P. Thieberger, K. Wikstr6m and G. Astner, Phys. Lett. 32B (1970) 476 3) I. BergstrOm, B. Fant, A. Filevich, G. Lind6n, K.-G. Rensfelt, J. Sztarkier and K. Wikstr6m, Research Institute for Physics, Stockholm, annual report (1970) pp. 78, 96 4) J. M. Jaklevic, C. M. Lederer and J. M. Hollander, Phys. Lett. 29B (1969) 179 5) J. B. Ball, J. B. McGrory, R. L. Auble and K. H. Bhatt, Phys. Lett. 29B (1969) 182 6) J. Picard and G. Bassani, Nucl. Phys. A131 (1969) 636 7) R. L. Kozub and D. H. Youngblood, Phys. Rev. C4 (1971) 535 8) H. Ejiri, S. M. Ferguson, I. Halpern and R. Heffner, Phys. Lett. 29B (1969) 111 9) P. J. Riley, J. L. Horton, C. L. Holles, S. A. Zaidi, C. M. Jones and J. L. Ford, Phys. Rev. C4 (1971) 1864 10) M. S. Zisman and B. G. Harvey, Phys. Rev. C4 0971) 1809 11) C. M. Lederer, J. M. Hollander and I. Perlman, Table of isotopes, 6th ed. (Wiley, New York, 1967) 12) H. Ohnuma and J. L. Yntema, Phys. Rev. 176 (1968) 1416 13) K. T. Kn6pfle, M. Rogge, C. Mayer-B6ricke, J. Pedersen and D. Burch, Nucl. Phys. A159 (1970) 642 14) K. Hesse and E. Finckh, Nucl. Phys. A141 0970) 417 15) F. Rauch, Z. Phys. 243 (1971) 105 16) S. Matsuki, Y. Yoshida, M. Hyakutake, M. Matoba, S. Nakamura and I. Kumabe, Nucl. Phys. A174 (9171) 343 17) D. L. Mathews, T. P. Lindsey, M. Koike and C. F. Moore, Phys. Rev. C4 (1971) 1876 18) G. T. Garvey, W. J. Gerace, R. L. Jaffe, I. Talmi and I. Kelson, Rev. Mod. Phys. 41 (1969) S1 19) M. Grecescu, A. Nilsson and L. Harms-Ringdahl, Research Institute for Physics, Stockholm, annual report (1970) p. 12 20) A. Nilsson and M. Grecescu, Nucl. Phys. A212 (1973) 448 21) S. A. Hjorth, H. Ryde and B. Sk~.nberg, Ark. Fys. 38 (1968) 537 22) I. Bergstr6m, C. J. Herrlander, A. Kerek and A. Luukko, Nucl. Phys. A123 0969) 99 23) T. Yamazaki and G. T. Ewan, Nucl. Phys. A134 (1969) 81
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