_ Proceedings of the International Conference _
"Nuclear Structure and Related Topics"
NATURE OF THE PYGMY RESONANCE IN CONTINUOUS 7 SPECTRA
© 2004 A. V. Voinov1)*. A.Schiller2), E. Algin2)'3)'4)'5), L. A. Bernstein2), P. E. Garrett2), M. Guttormsen6), R. 0. Nelson7), J. Rekstad6), S. Siem6)
Received January 21, 2004
Two-step-cascade spectra of the 171 Yb(n, 77)172Yb reaction have been measured using thermal neutrons. They are compared to calculations based on experimental values of the level density and radiative strength function obtained from the 173Yb(3He, aj)172Yb reaction. The multipolarity of a 6.5(15) ¡jNn resonance at 3.3(1) MeV in the strength function is determined to be M1 by this comparison.
Excited nuclei decay often by a cascade of 7 rays. While the decay between discrete states is determined by the details of the nuclear wave functions, unresolved transitions are best described by statistical concepts like a continuous radiative strength function (RSF) and level density. The RSF (reviewed in [1]) provides the mean value of the decay probability for a given 7-ray energy EY. For hard 7 rays, (~7—20 MeV), the RSF is governed by the giant electric dipole resonance whose parameters are determined from photoabsorption [2]. The soft tail of the RSF has been investigated by a variety of methods, most notably by primary 7 rays [3]. Recently, systematic studies of the soft RSF have been performed at the Oslo Cyclotron Laboratory using a method based on sequential extraction. With this method it is possible to obtain both the level density and RSF by a deconvolution of a set of primary 7 spectra from a range of excitation energies [4]. Total RSFs (summed over all multipolarities) of rare-earth nuclei can be extracted for Bn > EY > 1 MeV [5]. Their common, most striking feature is a resonance at EY ~ 3 MeV which is believed to be of dipole multipolarity but whose electromagnetic character is unknown. It has been shown for all investigated rare-earth nuclei that the total RSF is most readily decomposed into a sum of the Kadmenskii—Markushev—Furman (KMF) E1 model [6], a spin-flip M1 model [7], and the aforementioned soft dipole resonance [5]. The knowledge
1)Frank Laboratory of Neutron Physics, JINR, Dubna, Russia.
2)Lawrence Livermore National Laboratory, USA.
3)North Carolina State University, Raleigh, USA.
4)Triangle Universities Nuclear Laboratory, Durham, USA.
5)Department of Physics, Osmangazi University, Meselik, Turkey.
6)Department of Physics, University of Oslo, Norway.
7)Los Alamos National Laboratory, USA. E-mail: voinov@nf.jinr.ru
of the character of this resonance is essential for its theoretical interpretation. Experimentally, it can be determined from an auxiliary two-step-cascade (TSC) measurement [8].
The TSC method is based on the observation of decays from an initial state i to a final state f via intermediate level m [9—11]. A convenient initial state is that formed in thermal or average resonance capture (ARC); the final state can be any low-lying discrete state. TSC spectra are determined by the branching ratios of the initial and intermediate states (expressed as ratios of partial to total widths r) and by the level density p of intermediate states with spin and parity Jm:
hf (e1,e2) =
(1)
£
xl,xl'jn
rf„№) rff(ifr)
p py^mi <Jm) p
r i r m
+
+ -r-P\hm',<Jm>)-
XL,XL',J
m
ri
rr
The sums in Eq. (1) are restricted to give valid combinations of the level spins and parities and the transition multipolarities XL. They arise since one determines neither the ordering of the two 7 rays, nor the multipolarities of the transitions nor the spins and parities of the intermediate levels, hence one has to include all possibilities. The two transition energies are correlated by Ei + E2 = Ei — Ef, thus, TSC spectra can be expressed as spectra of one transition energy Ey only. TSC spectra are symmetric around EY7m = (Ei — Ef)/2; integration over EY yields twice the total TSC intensity Iif (if both 7 rays are counted in the spectrum). The knowledge of the parities ^i8) and nf ensures that Iif depends, roughly speaking,
8)One assumes that only neutron s capture occurs.
1891
7
on the product of two RSFs around EY/m [8] (i.e., E + /mi for ni = nf and 2/e/ 1 for n = nf, the latter case being more sensitive to the character of the soft resonance). Iif depends also on the level density. This usually prevents one from drawing firm conclusions from TSC experiments alone [11]. A combined analysis of Oslo-type and TSC experiments, however, will enable one to establish the sum and product, respectively, of all contributions to fM 1 and fE1 at energies of the soft resonance, thus determining its character. For this goal, the partial widths of Eq. (1) are expressed via
rXLy E ) = /xl(eY )Ef+1 Dx (2)
in terms of RSFs and level spacings Dx. Equation (2) actually gives only the average value of the PorterThomas distributed partial widths [12]. The total width r is the sum of all partial widths. Again, the sum is only the sum of mean values, however, the distribution of total widths with many components is almost ¿-like [12]. The level density for a given spin and parity is calculated from the total level density by [13]
p(Ex,.rx) = p(Ex)1-2-^±±exp [~{Jx+^l2?
(3)
where a is the spin cutoff parameter, and we assume equal numbers of positive and negative parity levels. This assumption and Eq. (3) have been verified from the discrete level schemes of rare-earth nuclei. Thus, all quantities for calculating TSC spectra are based on experimental data.
The combined analysis is applied to the nucleus 172Yb which has been investigated by the 173Yb(3He, a^)172Yb reaction in Oslo and by the 171Yb(n, yy)172Yb reaction at the Lujan Center of the Los Alamos Neutron Science Center (LANSCE). The Oslo data have been reported in [4, 5]. Thus, only a short summary is given. The experiment was performed using a 45-MeV 3He beam on a metallic, enriched, self-supporting target. Ejectiles were detected and their energies were determined using particle telescopes at 45°. In coincidence with a particles, y rays were detected in an array of NaI detectors. From the reaction kinematics, a energy is converted into Ex, and y-cascade spectra are constructed for a range of Ex bins. The y spectra are unfolded [14] and the primary y spectra are extracted using a subtraction method [15]. The spectra are deconvoluted into a level density and a total RSF by applying the Brink—Axel hypothesis [16]. The level density is normalized by comparison to discrete levels at low Ex and to the average neutron resonance spacing at Bn [4]. The RSF is normalized using the average total width
of neutron resonances, and is decomposed into the KMF E1 model [6], a spin-flip M1 model [7], and a soft dipole resonance [5]. Here, we have improved on the normalization of the level density and the RSF and included an isoscalar Lorentzian E2 model [17] giving
/tot = K (/E1 + /m 1) + EY /E2 + /soft, (4)
where K is a scaling factor of the order of one. Since quadrupole transitions populate levels within a broader spin interval than dipole transitions, Eq. (4) is of an approximative nature. Given the weakness of quadrupole transitions and the level of experimental uncertainties, however, this approximation is believed to be sufficient. The improved data, the fit to the total RSF, and its decomposition into different multipo-larities are given in Fig. 1. The parameters for the E1 RSF are taken from [5], those for the M1 and E2 RSFs from [7], where we use the fE1//M 1 sys-tematics at MeV giving values in agreement with ARC work [19]. The fit parameters are: the constant temperature of the KMF model T = 0.34(3) MeV, the normalization coefficient K = 1.7(1), and the three parameters of the soft resonance E = 3.3(1) MeV, r = 1.2(3) MeV, and a = 0.49(5) mb9).
For the 171Yb(n, yy)172Yb experiment, we used g of enriched, dry Yb2O3 powder encapsulated in a glass ampule, mounted in an evacuated beam tube and irradiated by collimated neutrons with a time-averaged flux of ^4 x 104 neutrons/(cm2 s) at ^20 m from the thermal moderator. Gamma rays were detected by two 80% and one shielded and segmented ^200% clover Ge(HP) detector, placed at ~12 cm from the target in a geometry to minimize angular correlation effects and contributions from higher multiplicity cascades. Single and coincident y rays were recorded simultaneously, including n time-of-flight and y—y coincidence time. The experiment ran for ^150 h yielding ~107 coincidences. The relative detector efficiencies from 1—9 MeV were determined by two separate runs of ^12 h each, before and after the 171 Yb(n, yy)172Yb experiment, using the 35Cl(n, y)36Cl reaction and its known y intensities [20]. Also, a standard calibrated 60Co source has been measured to adjust the relative curves to an absolute scale. The energy-summed coincidence spectrum (Fig. 2, upper panel) shows distinct peaks corresponding to TSCs between Bn and several low-lying states. The two strongest peaks have ^4000 counts each. TSC spectra (lower panels) were
9)The cited parameters are mean values obtained from the 173Yb(3He, a^)172Yb and 172Yb(3He,3He'Y)172Yb reaction data.
Level density, MeV 1
106
NATURE OF THE PYGMY RESONANCE Radiative strength, MeV-3
1893
104
102
4 6
Excitation energy, MeV
EY , MeV
Fig. 1. (Left) Total level density (circles), constant-temperature extrapolation (solid line), level density at Bn derived from the average neutron resonance spacing (square) [7], and level density from counting of discrete levels (jagged line) [18]. (Right) Total RSF (circles), fit to the data, and decomposition into RSFs of different multipolarities (solid curves). The inclusion of the soft resonance in the fit decreases the x?ed from ~7.4 to ~1.3. Since this value is close to unity, inclusion of additional nonstatistical structures cannot significantly improve the fit.
obtained by gating on three peaks, using the background
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