The $^{89}$Y($\alpha$, 2n$\gamma$)$^{91}$Nb reaction was used to populate excited states in $^{91}$Nb. The rotation of the angular distribution of the 357 keV gamma-transition from the 21/2$^{+}$ state was measured in an external magnetic field. The IPAD method was used. By applying $\tau$ =(1.33$\pm$ 0.14) ns for the lifetime of the 21/2$^{+}$ state at 3467 keV, the value of the g-factor 1.18 $\pm$ 0.18 was derived

Bałanda, Andrzej

Flak, E.

Kulessa, Reinhard

Rybicka, M.

Styczeń, J.

Wodniecki, P.

Acta Physica Polonica B

English

Jagiellonian Univeristy Repository

Vol. B8 (1977) ACTA PHYSICA POLONICA No 2THE g-FACTOR OF THE 21∕2+ STATE IN 91NbBy A. Balanda, E. Flak, R KulessaInstitute of Physics, Jagellonian University, Cracow** Address: Instytut Fizyki UJ, Reymonta 4, 30-059 Kraków, Poland.M. Rybicka, J. Styczeń and P. WodnieckiInstitute of Nuclear Physics, Cracow(Received July 16, 1976)The 89Y(≈, 2πy)91Nb reaction was used to populate excited states in 91Nb. The rotation of the angular distribution of the 357 keV gamma-transition from the 21∕2, state was measured in an external magnetic field. The IPAD method was used. By applying τ = (1.33 + 0.14) ns for the lifetime of the 21∕2+ state at 3467keV, the value of the ^'-factor 1.18 ±0.18 was derived.1. IntroductionThe properties of the N = 50 isotones have been succesfully described by the shell model treating 88Sr as an inert core and the valence protons as being restricted to the 2pi/2 and lg9/2 orbits [l-6]. In such configuration space the three valence protons in 9,Nb can have the P1,2(g9∕2)2> (pi/2)2 g9∕2 a∏d (g9/2)3 configurations. Of the three configura­tions, the last is the only one for which such a spin value as 21/2 can be obtained in the framework of the pure shell model.The level scheme as well as electromagnetic properties of the 91Nb nucleus have recently been studied in several experiments [7-12]. Nearly all levels belonging to the (g9,2)3 and all of the pł/2 (g9∕2)2 proton configurations have been found [10].For the 13∕2- state at 1985 keV the g-factor was determined by Feastermann et al. [11] and their experimental result was interpreted in terms of the ∣π(g9∕2)2 P1∕2, 13∕2> configu­ration. Recently Schneider et al. [12] have measured the half-life of the lowest 21∕2+ state at 3467 keV in 91Nb with the pulsed-beam direct-timing method. The result is Ti/2 = (0.92+0.10) ns. In their work both the experimental and theoretical E2 transition rates were derived and it was suggested that the 21/2+ → 17∕2+ transition in 9,Nb might not be very sensitive to configuration admixtures. It was hoped that the measurements of the g-factor for the 21∕'2+ state could furnish some further information concerning the configuration of this state.(147)1482. ExperimentalThe measurements were performed on the alpha beam of the U-120 cyclotron in the Institute of Nuclear Physics in Cracow. The experimental conditions were similar to those described elsewhere [13]. Alpha particles with an energy of 26.5 MeV bombarded a target with 89Y. The target used in the present experiment consisted of thin natural 89Y 2 mg∕cm2 foil with Bi backing of 200 mg∕cm2 to stop the alpha beam. The target was placed within the pole pieces (8 mm diam.) of an electromagnet whose magnetic field was applied perpendicularly to the reaction plane. The intensity of the field in the target place was measured with a well calibrated Hole probe.Fig. 1. Angular distribution for the 357 keV y-1ine deexcitating the 21∕2+ state at 3467 keV in 91 NbThe IPAD experiments were performed for three values of the magnetic field, i.e. for 9.5, 11.2 and 12.15 kGs the directions of which were automatically reversed every two minutes during the measurements.The angular distribution of the 357 keV y-ray deexciting the 21∕2+ level at 3467 keV was measured by a 13 cm3 Ge(Li) detector mounted on a turn-table at a distance of 90 mm from the target. An NaJ(Tl) counter placed at 90° to the beam direction acted as a monitor. The intensities of the y-ray measured with the movable detector were further corrected for absorption in the target (see paragraph 3); the correction factors were calculated from the known Y and Bi thicknesses. These factors were also verified using a radioactive source placed at the beam position after the experiment. An example of the angular distri­bution measured for the 357 keV transition is shown in Fig. 1.149The measurements of the angular distribution of the 357 keV gamma-transition for the two opposite directions of the external magnetic field provided two sets of data: Ai(d) and N~(θ). As has been mentioned earlier, the magnetic field direction during the experiment was changed very frequently. Owing to the monitor detector, moreover, it was certain that the N+(θ) and N~~(θ) values were properly normalized. Then, after the normalization at each angle for time and beam intensity and the absorption in the target, they could be fitted with the two Wi(θ) functions which are given by two following ex-The angle 9 denotes rotation of the beam axis according to the field direction. This effect is due to the bending of the α beam in the stray magnetic field.In the present work, however, instead of analysing the experimental data with these Hzi(0) functions, the values of new functions R(θ) and HZ-(Θ) were calculated from N+(θ) and N~(θ) quantities, whereK((?) = N+(0)-N-(,θ)“ N+(0) + N~(θ) (2)and lF+(0) = k(0)N + (Θ') +k(0)N~(0). (3)An example of the experimental 7?(0) function is shown in Fig. 2. The coefficients k{θ) are the normalization coefficients which involve for each angle the time and beam intensity differences and the absorption in the target. The present way of handling the data provides a more reliable method to obtain the ωτ value, since one can avoid the normalization of the experimental N+(θ) and N(0) peak intensities at every angle 0 in the calculation of the R(θ) curve. The normalization is crucial in the case of Wi(θ) curves, when they are used to provide the ωτ value, whereas it can be dispensed with in the R(θ) function which, as will be shown below, depends directly on ωτ.The normalization had to be taken into account in the Hz+(0) curve calculated in the present work, or when W(ff) was measured without the external magnetic field in the same experimental conditions in which the R(Θ) curve was obtained. It was observed in the testing fits that an increase of the errors on the experimental W+(β) points (i.e. on the experimental W~(0) and W~(θ)) by a factor of two did not cause a similar increase of the error on ωτ when the fit was made with the R(θ) and W÷(0) functions. On the other-hand the ωτ error obtained was two times larger when the fit was made with the functions given 3. Data analysis(1)pressionswhereand150by Eq. (1) to the Wi(()) values. This shows that the normalization would cause a greater effect on ωτ if the analysis was made with !Ti(0) functions.The computer fits were made with a MULT program [14]. The program permits to perform a simultaneous fit of two types of mathematical functions to the appropriate experimental points. Inserting in the expression (2) the functions (1) one obtainsR(0) = ∑ b'k sin kθ sin k∆kθ k even1 + ∑ b'k cos kθ cos k∆kθ k even(4)Fig. 2. MeasuredΛΓ+(θ)-Λt-(θ)N+(θ)+N~(θ)Λ(Θ) = 2 at Bo = 12.15 kGs external magnetic field. The solid linerepresents a common fit (see text)Limiting the summation at k = 4 and taking into account the fact that the angle 9 due to the beam bending is of the order of one degree, the R(θ) function can be written asR(θ) = 4 b2 sin 20 + 2^4 sin 401 + b,2 cos 20+b,4 cos 40 (9 + ωτ). (5)The H^(fi) function was then given by the following expressionJF+(O) = ff0(l + b'2 cos 20 + h4 cos 40). (6)The values of the angle 9 = 0.0183, 0.0216 and 0.0234 were calculated by numerical integration over the magnetic field profiles f(s) obtained for the Bo = 9.5,11.2 and 12.15 kGs fields applied. This angle was calculated using the following formula,9 = 6.942 x 10 -3 B0[kGs] √Ea[MeV]00 (7)151Besides this rotation of the beam axis according to the field direction there is also a shift of the beam spot. This latter effect was also taken into account in the JVzt(0)peak intensities measured at every angle θ.The weighted average of the gτ product obtained from the experimental data for the three external fields isgτ = 1.567±0.167.Applying the lifetime τ = (1.33 + 0.14) ns gives the following value of the g-factor of the 21/2+ stateg = 1.18 + 0.18.4. DiscussionThe assumption of the pure (g9/2)3 shell model configuration for the 21∕2^~ state in 91Nb would lead to a g-factor for this state equal to the Schmidt limits, i.e. 1.5085, according to the additivity relation [15]. The known g-factors for the (g9 2)" configurations in the 88Sr region obtained from the experimental magnetic moments measured for the states 8÷ in 90Zr, 9/2*  in 93Nb and 8? in 92Mo deviate from the Schmidt value [15], Of those three g-factors, the one for 90Zr, g = 1.364+0.019, is considered to correspond to almost pure configuration of (gg<2)2 while for the (g9∕2)3 configuration the value of g = 1.371 was obtained from the measured magnetic moment of the 9∕2+ ground state of 93Nb [16].The present g-factor, g = 1.18 + 0.18, for the 21/2*  state in 91Nb seems to be lower than that value. However, there is a relativly high uncertainty, which is due to the large error in the mean lifetime of this state and the necessity to employ the integral PAD method.The authors would like to thank Professor S. Ogaza and dr E. Bożek for many helpful discussions. Sincere thanks are also due to the Staff of the U-120 Cyclotron for providing its excellent operating conditions.references[1] S. Cohen, R. D. Lawson, H. M. Macfarlane, M. Soga, Phys. Lett. 9, 180 (1964).[2] N. Auerbach, 1. Talmi, Nucl. Phys. 64, 458 (1965).[3] J. Vervier, Nucl. Phys. 75, 17 (1966).[4] J. B. Ball, J. B. Me Grory, J. S. Larsen, Phys. Lett. 41B, 581 (1972).[5] D. H. Gloeckner, F. J. D. Serduke, Nucl. Phys. A220, 477 (1974).[6] A. Balanda, to be published.[7] M. Grecescu, A. Nillsson, L. Harms-Ringdahl, Nucl. Phys. A212, 429 (1973).[8] A Berinde, R. O. Dumitru, M. Grecescu, A. Iordacescu, I. Neamu, G. Pasco vici, D. Piosti- naru, T. C. Teodorescu, Z. Phys. 269, 117 (1974).[9] B. A. Brown, P. M. Lesser, D. B. Fossan, Phys. Rev. Lett. 34, 161 (1975).[10] A. Balanda, R. Kulessa, W. Waluś, J. Sieniawski, Acta Phys. Pol. B7, 355 (1976).[11] T. Faestermann, F. Feilitzch, M. R. Maier, P. Raghavan, R. S. Raghavan, C. Signorini, Nucl. Phys. MS1, 135 (1976).[12] W. D. Schneider, K. H. Gonsior, C. Giinther, Nιιcl. Phys. A249, 103 (1975).152[13] E. Bożek, B. Haas, B. Ingarden-Dutkiewicz, K. Królas, J. C. Medinger, J. Styczeń, J. P. Vievien, Nuci. Phys., in print.[14] Z. Stachura, to be published.[15] Shoji Nagamiya, Scientific Papers of the Inst, of Physical and Chemical Reaserch — Japan 66, 39 (1972).[16] V. S. Shirley, Table of Nuclear Moments in Hyperfine Inter, in Excited Nuclei, ed. G. Goldring and R. Kalish, Gordon and Breach, New York 1971, p. 1255.

The g-factor of the 21/2$^{+}$ state in $^{91}$Nb

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The g-factor of the 21/2 $^{+}$ state in $^{91}$ Nb

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The g-factor of the 21/2+^{+}+ state in 91^{91}91Nb

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The g-factor of the 21/2 $^{+}$ state in $^{91}$ Nb