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Unformatted text preview: Journal of the Korean Physical Society, Vol. 56, No. 1, January 2010, pp. 28 ∼ 33 Empirical Formula Extended to the Yrast Excitation Energies of the Unnatural Parity States in Even-Even Nuclei Dooyoung Kim , Jin-Hee Yoon and Dongwoo Cha * Department of Physics, Inha University, Incheon 402-751 (Received 26 October 2009, in final form 17 November 2009) Recently, it was shown that a simple empirical formula, in terms of the mass and the valence nucleon numbers, could describe the main trends of the yrast excitation energies of the natural parity states up to 10 + in even-even nuclei throughout the entire periodic table. The same empirical formula was applied to the yrast excitation energies of the unnatural parity states, including 1 + , 2- , 3 + , 4- , 5 + , 6- , 7 + , 8- , 9 + , 10- , and 11 + , in even-even nuclei. Although the overall character of the effective residual interaction for the unnatural parity states was quite different from that of the natural parity states, the same form of the empirical formula was found to hold reasonably well for the yrast excitation energies of the unnatural parity states. PACS numbers: 21.10.Re, 23.20.Lv Keywords: Empirical formula, Lowest excitation energies of unnatural parity states, Valence nucleon num- bers DOI: 10.3938/jkps.56.28 I. INTRODUCTION We benefit sometimes by examining particular nuclear properties in terms of simple nuclear variables over a wide span of the chart of nuclides. The oldest well- known example is the Weizs¨ acker’s semi-classical mass formula, which can reproduce the binding energy of the ground state of nuclei quite accurately in terms of the mass number A and the atomic number Z [1]. Another well known study revealed the so-called N p N n scheme, where N p and N n are the valence proton and neutron numbers, respectively. The N p N n scheme denotes the phenomenon of a simple pattern that occurs when the nuclear data related to the lowest collective states are plotted against the product N p N n . The N p N n scheme has been used extensively and successfully for more than two decades to correlate the large volume of data on the collective degrees of freedom in nuclei [2]. Recently, another study devised an empirical formula by also adopting the valence nucleon numbers to express the yrast excitation energies of the electric quadrupole ( E 2) states in even-even nuclei throughout the entire periodic table [3]. Later, the same formula was shown to be capable of describing the main trends of the yrast excitation energies of not only the E 2 states but also the natural parity, even multipole states up to 10 + found in all even-even nuclei [4]. In addition, it was demon- strated that this empirical formula complied with the N p N n scheme, even though the empirical formula itself * E-mail: [email protected]; Fax: +82-32-866-2452 did not explicitly depend on the product N p N n [5]. Sub- sequently, the empirical formula was tested successfully for the yrast excitation energies of natural parity odd...
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article3 - Journal of the Korean Physical Society, Vol. 56,...

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