Exploration of resonances by using complex momentum representation

Ya-Juan Tian; Tai-Hua Heng; Zhong-Ming Niu; Quan Liu; Jian-You Guo

doi:10.1088/1674-1137/41/4/044104

Chinese Physics C> 2017, Vol. 41> Issue(4) : 044104 DOI: 10.1088/1674-1137/41/4/044104

Exploration of resonances by using complex momentum representation

1.
School of Physics and Materials Science, Anhui University, Hefei 230601, China

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Abstract：
Resonance research is a hot topic in nuclear physics, and many methods have been developed for resonances. In this paper, we explore resonances by solving the Schrödinger equation in complex momentum representation, in which the bound states and resonant states are separated completely from the continuum and exposed clearly in the complex momentum plane. We have checked the convergence of the calculations on the grid numbers of the Gauss-Hermite quadrature and the Gauss-Legendre quadrature, and the dependence on the contour of momentum integration. Satisfactory results are obtained. ¹⁷O is chosen as an example, and we have calculated the bound and resonant states to be in excellent agreement with those calculated in the coordinate representation.
- single-particle levels ,
- resonant states ,
- complex momentum representation

References

[1]	Wikipedia, https://en.wikipedia.org/wiki/Resonance
[2]	J. Meng and P. Ring, Rev. Lett., 77:3963 (1996)
[3]	W. Pschl, D. Vretenar, G.A. Lalaziss, and P. Ring, Phys. Rev. Lett., 79:3841 (1997)
[4]	N. Sandulescu, N. Van Giai, and R.J. Liotta, Phys. Rev. C, 61:061301 (2000)
[5]	J. Meng and P. Ring, Phys. Rev. Lett., 80:460 (1998)
[6]	Y. Zhang, M. Matsuo, and J. Meng, Phys. Rev. C, 86:054318 (2012)
[7]	S. G. Zhou, J. Meng, P. Ring, and E. G. Zhao, Phys. Rev. C, 82:011301 (2010)
[8]	A. S. Jensen, K. Riisager, D. V. Fedorov, and E. Garrido, Rev. Mod. Phys., 76:215 (2004)
[9]	E. P. Wigner and L. Eisenbud, Phys. Rev., 72:29 (1947)
[10]	A. U. Hazi and H. S. Taylor, Phys. Rev. A, 1:1109 (1970)
[11]	J. R. Taylor, Scattering Theory:The Quantum Theory on Nonrelativistic Collisions (John Wiley Sons, New York, 1972)
[12]	E. J. Heller and H. A. Yamani, Phys. Rev. A, 9, 1201 (1974); E. J. Heller and H. A. Yamani, ibid. 9:1209 (1974)
[13]	V. I. Kukulin, V. M. Krasnopl'sky, and J. Horček, Theory of Resonances:Principles and Applications (Kluwer, Dordrecht, 1989)
[14]	J. Humblet, B. W. Filippone, and S. E. Koonin, Phys. Rev. C, 44:2530 (1991)
[15]	B. N. Lu, E. G. Zhao, and S. G. Zhou, Phys. Rev. Lett., 109:072501 (2012)
[16]	B. N. Lu, E. G. Zhao, and S. G. Zhou, Phys. Rev. C, 88:024323 (2013)
[17]	E. N. Economou, Green's Function in Quantum Physics (Springer-Verlag, Berlin, 2006)
[18]	T. T. Sun, S. Q. Zhang, Y. Zhang, J. N. Hu, and J. Meng, Phys. Rev. C, 90:054321 (2014)
[19]	J. Aguilar and J. M. Combes, Commun. Math. Phys., 22:269 (1971); E. Balslev and J.M. Combes, Commun. Math. Phys., 22:280 (1971); B. Simon, Commun. Math. Phys, 27:1 (1972)
[20]	K. Arai, Phys. Rev. C, 74:064311 (2006)
[21]	N. Michel, W. Nazarewicz, M. Ploszajczak, and T. Vertse, J. Phys. G:Nucl. Part. Phys., 36:013101 (2009)
[22]	N. Michel, K. Matsuyanagi, and M. Stoitsov, Phys. Rev. C, 78:044319 (2008)
[23]	A. T. Kruppa, G. Papadimitriou, W. Nazarewicz, and N. Michel, Phys. Rev. C, 89:014330 (2014)
[24]	A. T. Kruppa, P. H. Heenen, H. Flocard, and R. J. Liotta, Phys. Rev. Lett., 79:2217 (1997)
[25]	N. Moiseyev, Phys. Rep., 302:212 (1998)
[26]	T. Myo, Y. Kikuchi, H. Masui, and K. KatŌ, Prog. Part. Nucl. Phys., 79:1 (2014)
[27]	J. Carbonell, A. Deltuva, A.C. Fonseca, and R. Lazauskas, Prog. Part. Nucl. Phys., 74:55 (2014)
[28]	J. Y. Guo, M. Yu, J. Wang, B. M. Yao, and P. Jiao, Comput. Phys. Commun., 181:550 (2010)
[29]	J. Y. Guo, X. Z. Fang, P. Jiao, J. Wang, and B. M. Yao, Phys. Rev. C, 82:034318 (2010)
[30]	Z. L. Zhu, Z. M. Niu, D. P. Li, Q. Liu, and J. Y. Guo, Phys. Rev. C, 89:034307 (2014)
[31]	M. Shi, Q. Liu, Z. M. Niu, and J. Y. Guo, Phys. Rev. C, 90:034319 (2014)
[32]	Q. Liu, J. Y. Guo, Z. M. Niu, and S. W. Wan, Phys. Rev. C, 86:054312 (2012)
[33]	L. Zhang, S. G. Zhou, J. Meng, and E. G. Zhou, Phys. Rev. C, 77:014312 (2008)
[34]	T. Berggren, Nucl. Phys. A, 109:265 (1968)
[35]	G. Hagen and J. S. Vaagen, Phys. Rev. C, 73:034321 (2006)
[36]	A. Deltuva, Few-Body Syst., 56:897 (2015)
[37]	C. V. Sukumar, J. Phys. A, 12:1715 (1979)
[38]	Y. R. Kwon and F. Tabakin, Phys. Rev., 18:932 (1978)
[39]	R. J. Liotta, E. Maglione, N. Sandulescu, T. Vertse, Phys. Lett. B, 367:1 (1996)
[40]	N. Michel, W. Nazarewicz, M. Ploszajczak, and K. Bennaceur Phys. Rev. Lett., 89:042502 (2002)
[41]	Niu Li, Min Shi, Jian-You Guo, Zhong-Ming Niu, and Haozhao Liang, Phys. Rev. Lett., 117:062502 (2016)
[42]	I. Hamamoto, Phys. Rev. C, 85:064329 (2012)
[43]	A. Bohr and B. R. Mottelson, Nuclear Structure (Benjamin, Reading, MA, 1969), Vol. I

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Ya-Juan Tian, Tai-Hua Heng, Zhong-Ming Niu, Quan Liu and Jian-You Guo. Exploration of resonances by using complex momentum representation[J]. Chinese Physics C, 2017, 41(4): 044104. doi: 10.1088/1674-1137/41/4/044104

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Received: 2016-09-29

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Supported by National Natural Science Foundation of China (11575002, 11175001, 11205004, 11305002), Program for New Century Excellent Talents at the University of China (NCET-05-0558), Natural Science Foundation of Anhui Province (1408085QA21), Key Research Foundation of Education Ministry of Anhui Province of China (KJ2016A026), and 211 Project of Anhui University

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通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

Exploration of resonances by using complex momentum representation

Corresponding author: Jian-You Guo,

1. School of Physics and Materials Science, Anhui University, Hefei 230601, China

Received Date: 2016-09-29

Available Online: 2017-04-05

Fund Project: Supported by National Natural Science Foundation of China (11575002, 11175001, 11205004, 11305002), Program for New Century Excellent Talents at the University of China (NCET-05-0558), Natural Science Foundation of Anhui Province (1408085QA21), Key Research Foundation of Education Ministry of Anhui Province of China (KJ2016A026), and 211 Project of Anhui University

Abstract: Resonance research is a hot topic in nuclear physics, and many methods have been developed for resonances. In this paper, we explore resonances by solving the Schrödinger equation in complex momentum representation, in which the bound states and resonant states are separated completely from the continuum and exposed clearly in the complex momentum plane. We have checked the convergence of the calculations on the grid numbers of the Gauss-Hermite quadrature and the Gauss-Legendre quadrature, and the dependence on the contour of momentum integration. Satisfactory results are obtained. ¹⁷O is chosen as an example, and we have calculated the bound and resonant states to be in excellent agreement with those calculated in the coordinate representation.

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Exploration of resonances by using complex momentum representation

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