Gaussian polynomial method for spin-dependent level density and new formula for spin distribution

Paar, V.; Sunko, D. K.; Brant, S.; Mustafa, Munshi G.; Lanier, R.G.

doi:10.1007/bf01282895

Cited by 19 publications

(6 citation statements)

References 91 publications

(150 reference statements)

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“…[52] suggesting η = 0.75 for 51 V, a lot of successful model calculations with η = 0.5 in the medium mass region, and our conclusion of η = 0.25 for heavy nuclei, all agree quite well with the data calculated from Eq. (11) [η(51) = 0.63, η(100) = 0.50, η(197) = 0.30]. Since energy dependence for η has not been observed, the results of the low-energy analysis can be extended to higher excitation energies, and we can postulate that η has a mass dependence even up to mass number 197.…”

Section: Discussionmentioning

confidence: 97%

“…Recent theoretical studies are based on the microscopic statistical model [9,10], which is beginnig to approach the quality of the semiempirical models, but its results are available only in the form of numerical data. Theoretical studies have shown that the spin dependence of the level density can deviate from the simple formula given above at a high spin [11]. Studies of the spin distribution are interesting both from the theoretical [12] and experimental points of view.…”

Section: Introductionmentioning

confidence: 96%

See 1 more Smart Citation

Cross sections for the formation ofHg195m,g,
Sudár
¹
,
Qaim
²

2006
Phys. Rev. C

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Excitation functions were measured for the reactions nat Pt( 3 He, xn) 195 Hg m,g , nat Pt( 3 He, xn) 197 Hg m,g , nat Pt( 3 He, x) 196 Au m,g , and nat Pt(α, xn) 197 Hg m,g over the energy range of 18-35 MeV for 3 He particles and 17-26 MeV for α particles. The reactions 197 Au(p, n) 197 Hg m,g were also investigated over the proton energy range of 6-20 MeV. The three projectiles were produced at the Jülich variable-energy compact cyclotron (CV 28). Use was made of the activation technique in combination with conventional high-resolution as well as low-energy HPGe-detector γ -ray spectroscopy. For most of the reactions, the present measurements provide the first consistent sets of data. From the available experimental data, isomeric cross-section ratios were determined for the above-mentioned reactions. Nuclear model calculations using the code STAPRE, which employs the Hauser-Feshbach (statistical model) and exciton model (precompound effects) formalisms, were undertaken to describe the formation of both the isomeric and the ground states of the products. The calculations were compared with the results of the EMPIRE-II code. The excitation functions of the ( 3 He, xn) and (α, xn) processes are described well by the theory. In the case of ( 3 He, pxn) reactions, however, considerable deviations were observed between the experiment and the theory, presumably due to strong contributions from direct interactions. A description of the isomeric cross-section ratio by the model was possible only with a very low value of η, i.e., the eff / rig ratio. A mass dependence of η is proposed.

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Section: Discussionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 96%

Cross sections for the formation ofHg195m,g,
Sudár
¹
,
Qaim
²

2006
Phys. Rev. C

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“…Bethe approximated p(M ) with a Gaussian distribution (using the Central Limit Theorem) and assuming classical statistics for the particles constituting the nucleus [4]. This was a major drawback of his approach, as the constituent particles of a nucleus are really fermions, and thus the Bethe approximation can be used only for small values of the total angular momentum of the nucleus [18]. An improvement of this approximation uses the Edgeworth expansion (see e.g.…”

Section: Physical Applicationsmentioning

confidence: 99%

“…To approximate the distribution of M | N = N analytically, we calculate its mean, variance and kurtosis, and then use the fourth-order approximation (18). The calculation of the above moments is done recursively.…”

Section: B Quantum Particlesmentioning

confidence: 99%

Exact and approximate methods of calculating the sum of states for noninteracting classical and quantum particles occupying a finite number of modes

Werpachowska

2011

Phys. Rev. E

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We present exact expressions for the sum of states of noninteracting classical and quantum particles occupying a finite number of modes with arbitrary spacings. Exploiting a probabilistic analogy, we derive an analytic fourth-order approximation to the density of states, which captures its variance and kurtosis, and is superior to the previous, commonly used methods for all three particle statistics. Our approach employs a simple exact method of calculating the moments of the microcanonical density of states for quantum particles, which requires less computational effort than the commonly used saddle-point approximation. We test our methods numerically and discuss their applicability to various physical systems.

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“…Recent theoretical studies are based on microscopic statistical model [14,15] which is beginning to approach the quality of the semi-empirical models, but its results are available only in the form of numerical data. Theoretical studies have shown that for high spin values the spin dependence of the level density can deviate from the simple formula given above [16]. Studies on the spin distribution are interesting both from the theoretical [17] and experimental points of view.…”

Section: Introductionmentioning

confidence: 97%

Mass number and excitation energy dependence of the Θ /Θ parameter of the spin cut-off factor in the formation of an isomeric pair

Sudár

Qaim

2018

Nuclear Physics A

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The Θ ef f /Θ rig parameter of the spin distribution of the level density of an excited nucleus was determined for 61 nuclei covering the mass range of 44 to 200. The experimental isomeric crosssection ratios for 25 isomeric pairs were compared with the model calculation to find the best fit to the experimental data. An isomeric cross-section ratio may be affected by more nuclei depending on the reaction. The model calculations were carried out with the TALYS code using the backshifted Fermi gas model for the level density. The reduced χ 2 values were calculated to describe the deviation of the experimental data from the model calculation as a function of the η = Θ ef f /Θ rig parameter. The minimum of the reduced χ 2 curve defined the best probable Θ ef f /Θ rig parameter. An η d was introduced calculating the Θ ef f /Θ rig value from the low energy discrete levels of the nucleus. The η/η d values seem to be independent of the mass number, their average value near to one, but showing slight dependence on the odd-even characteristic of the proton and neutron number. The η/η d values also seem to be independent of the average excitation energy in the continuum, indicating that η is independent of the excitation energy. The mass number and (N-Z) dependence of the η values were studied. The η values for the nuclei with odd mass number show a characteristic exponential decrease as a function of the mass number or (N-Z). The η values for the odd-odd type of nuclei appear to be constant, near one, up to the mass number 110 or (N-Z) of 13. Above these values, the η values show characteristic exponential decrease like nuclei with the odd mass number. The η values for even-even type nuclei decrease exponentially up to A equal to 142 or (N-Z) equal to 20. The values are lower than those for the nearby odd-odd type nuclei.The η values increase for nuclei with A between 142 and 156 and (N-Z) between 20 and 28, and they finally reach the value of odd-odd type systematics. This behavior indicates some individual properties of the 156 Gd. The odd-even effect of Θ ef f /Θ rig may change the calculated activation cross section significantly in some energy regions.

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Gaussian polynomial method for spin-dependent level density and new formula for spin distribution

Cited by 19 publications

References 91 publications

Cross sections for the formation ofHg195m,g,
Sudár
¹
,
Qaim
²

2006
Phys. Rev. C

Cross sections for the formation ofHg195m,g,
Sudár
¹
,
Qaim
²

2006
Phys. Rev. C

Exact and approximate methods of calculating the sum of states for noninteracting classical and quantum particles occupying a finite number of modes

Mass number and excitation energy dependence of the Θ /Θ parameter of the spin cut-off factor in the formation of an isomeric pair

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Gaussian polynomial method for spin-dependent level density and new formula for spin distribution

Cited by 19 publications

References 91 publications

Cross sections for the formation ofHg195m,g,Sudár1, Qaim2 2006Phys. Rev. C

Cross sections for the formation ofHg195m,g,Sudár1, Qaim2 2006Phys. Rev. C

Exact and approximate methods of calculating the sum of states for noninteracting classical and quantum particles occupying a finite number of modes

Mass number and excitation energy dependence of the Θ /Θ parameter of the spin cut-off factor in the formation of an isomeric pair

Contact Info

Product

Resources

About

Cross sections for the formation ofHg195m,g,
Sudár
¹
,
Qaim
²

2006
Phys. Rev. C

Cross sections for the formation ofHg195m,g,
Sudár
¹
,
Qaim
²

2006
Phys. Rev. C