Two-proton emission from excited states of  proton-rich nuclei

Xing Feng-Zhu; Cui Jian-Po; Wang Yan-Zhao; Gu Jian-Zhong

doi:10.7498/aps.71.20211839

Abstract

The effective liquid drop model (ELDM) and the generalized liquid drop model (GLDM) are extended to the case of studying the two-proton (2p) radioactivity from the excited states of proton-rich nuclei. It is shown that the experimental 2p decay half-lives are reproduced well by the ELDM and the GLDM. Then, the 2p decay half-lives of excited states of some nuclei that are not yet available experimentally are predicted by the two models, which are useful for searching for the new 2p decay candidates in future. Meanwhile, the above predicted half-lives are analyzed and compared with those given by the unified fission model (UFM). Next, the influence of the uncertainties of the decay energy and the angular momentum on the half-lives are analyzed in the frame of the two models by taking the 2p radioactivity of the 21⁺ isomeric state of ⁹⁴Ag for example. It is found that the half-lives go up with the increase of the angular momentum, following the law of the quadratic function. Furthermore, the strong dependence of the half-lives on the decay energy suggests that it is important and necessary to measure accurately the mass value of the parent nucleus and the daughter nucleus and the excitation energy. Finally, it is necessary to point out that the existence of the 2p radioactivity in the 21⁺ isomeric state of⁹⁴Ag remains to be a mystery. Moreover, although the 2p radioactivity is observed from the higher excited states of ¹⁷Ne and ¹⁸Ne, the relevant hypotheses have not yet been further tested experimentally. The construction of a new generation of radioactive ion beam facilities, such as the high intensity heavy-ion accelerator facility (HIAF), is expected to be used to uncover the nature of the 2p radioactivity in the 21⁺ isomeric state of ⁹⁴Ag and further test the hypotheses of the 2p decay from the higher excited states of ¹⁷Ne and ¹⁸Ne. On the other hand, some microscopic models, such as the shell model, need to be further developed by including some necessary physical factors, such as the tensor force, three-body force and accurate pairing force, to describe the mechanism of the 2p emission of the excited states more reasonably. In summary, more nuclear structure information can be extracted by studying the 2p radioactivity of the excited states. It is worth studying further although it is rather difficult to observe.

Keywords:

Authors and contacts

1.
Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China
2.
Institute of Applied Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China
3.
China Institute of Atomic Energy, Beijing 102413, China

Corresponding author: Wang Yan-Zhao, yanzhaowang09@126.com ; Gu Jian-Zhong, jzgu1963@ciae.ac.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. U1832120, 11675265), the Natural Science Foundation of Hebei Province, China (Grant Nos. A2020210012, A2021210010), the Continuous Basic Scientific Research Project, China (Grant No. WDJC-2019-13), and the Leading Innovation Project, China (Grant No. LC192209000701).

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References

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Cited By

图 1 母核衰变过程中发射粒子和子核形状示意图

Figure 1. Schematic representation of the configuration of the emitted particle and daughter nucleus.

DownLoad: Full-Size Img PowerPoint

图 2 用ELDM 和GLDM计算的⁹⁴Ag的21⁺激发态的2p发射半衰期随l的演化情况, 阴影区域为半衰期的实验数据

Figure 2. The 2p decay half-lives of the 21⁺ isomeric state of ⁹⁴Ag within the ELDM and GLDM as functions of l. The shaded area stands for the experimental half-life.

DownLoad: Full-Size Img PowerPoint

表 1 激发态原子核2p发射半衰期的理论计算结果与实验值的比较

Table 1. Comparison between the experimental 2p decay half-lives of excited states and those within different models.

母核	子核	$J_{\text{i}}^{\text{π }}$	$J_{\text{f}}^{\text{π }}$	l	Q^Exp./MeV	${\lg}{T_{1/2} }/{\text{s} }$
母核	子核	$J_{\text{i}}^{\text{π }}$	$J_{\text{f}}^{\text{π }}$	l	Q^Exp./MeV	Exp.	ELDM	GLDM	UFM^[51]
¹⁴O*	¹²C	2⁺	0⁺	2	1.20^[8]	>–16.12^[8]	–15.49	–16.10	–16.02
		2⁺	0⁺	2	3.15^[8]		–18.22	–19.58	–18.87
		4⁺	0⁺	4	3.35^[8]		–16.25	–16.76	–15.96
¹⁷Ne*	¹⁵O	3/2^–	1/2^–	2	0.35^[9,10]	>–10.59^[10]	–6.98	–6.79	–7.11
		5/2^–	1/2^–	2	0.82^[9,10]		–12.41	–12.68	–12.73
		1/2⁺	1/2^–	1	0.97^[9,10]		–14.20	–14.68	–14.69
¹⁸Ne*	¹⁶O	2⁺	0⁺	2	0.59^[11]		–10.59	–10.96	–10.91
¹⁸Ne*	¹⁶O	1^–	0⁺	1	1.63^[11]	$ -16.15^{+0.06}_{-0.06} $^[11,12]	–16.34	–17.20	–16.79
²²Mg*	²⁰Ne	—	0⁺	0	6.11^[52,53]		–19.75	–19.58	–18.97
²⁹S*	²⁷Si	—	0⁺	0	1.72—2.52^[54]		–15.5— –13.4	–17.2— –14.7	–16.4— –14.3
²⁹S*	²⁷Si	—	0⁺	0	4.32—5.12^[54]		–18.4— –17.8	–19.2— –18.8	–18.9— –18.5
⁹⁴Ag*	⁹²Rh*	21⁺	11⁺	6—10	1.90^[55]	$ 1.90^{+0.38}_{-0.20} $^[55]	9.42—14.63	8.22—13.38	9.38—15.21
					1.98^[56]		8.61—13.80	7.41—12.55	8.56—14.37
					2.05^[56]		7.95—13.11	6.74—11.86	7.89—13.68
					3.45^[56]		–0.80—4.04	–2.03—2.75	–0.92—4.56

DownLoad: CSV

[1]	Goldansky V I 1960 Nucl. Phys. 19 482 Google Scholar
[2]	Goldansky V I 1961 Nucl. Phys. 27 648 Google Scholar
[3]	Cable M D, Honkanen J, Parry R F, et al. 1983 Phys. Rev. Lett. 50 404 Google Scholar
[4]	Blank B, Boue F, Andriamonje S, et al. 1997 Z. Phys. A: At. Nucl. 357 247
[5]	Honkanen J, Cable M D, Parry R F, et al. 1983 Phys. Lett. B 133 146 Google Scholar
[6]	Borrel V, Jacmart J C, Pougheon F, et al. 1987 Nucl. Phys. A 473 331 Google Scholar
[7]	Dossat C, Adimi N, Aksouh F, et al. 2007 Nucl. Phys. A 792 18 Google Scholar
[8]	Bain C R, Woods P J, Coszach R, et al. 1996 Phys. Lett. B 373 35 Google Scholar
[9]	Chromik M, Brown B A, Fauerbach M, et al. 1997 Phys. Rev. C 55 1676 Google Scholar
[10]	Chromik M J, Thirolf P G, Thoennessen M, et al. 2002 Phys. Rev. C 66 024313 Google Scholar
[11]	Gomez del Campo J, Galindo-Uribarri A, Beene J R, et al. 2001 Phys. Rev. Lett. 86 43 Google Scholar
[12]	Raciti G, Cardella G, De Napoli M, et al. 2008 Phys. Rev. Lett. 100 192503 Google Scholar
[13]	Goldansky V I 1988 Phys. Lett. B 212 11 Google Scholar
[14]	Pfützner M, Badura E, Bingham C, et al. 2002 Eur. Phys. J. A 14 279 Google Scholar
[15]	Giovinazzo J, Blank B, Chartier M, et al. 2002 Phys. Rev. Lett. 89 102501 Google Scholar
[16]	Dossat C, Bey A, Blank B, et al. 2005 Phys. Rev. C 72 054315 Google Scholar
[17]	Pomorski M, Pfützner M, Dominik W, et al. 2014 Phys. Rev. C 90 014311 Google Scholar
[18]	Wang M, Audi G, Kondev F G, et al. 2017 Chin. Phys. C 41 030003 Google Scholar
[19]	Pomorski M, Pfützner M, Dominik W, et al. 2011 Phys. Rev. C 83 061303(R
[20]	Blank B, Bey A, Canchel G, et al. 2005 Phys. Rev. Lett. 94 232501 Google Scholar
[21]	Ascher P, Audirac L, Adimi N, et al. 2011 Phys. Rev. Lett. 107 102502 Google Scholar
[22]	Goigoux T, Ascher P, Blank B, et al. 2016 Phys. Rev. Lett. 117 162501 Google Scholar
[23]	Whaling W 1966 Phys. Rev. C 150 836 Google Scholar
[24]	Jager M F, Charity R J, Elson J M, et al. 2012 Phys. Rev. C 86 011304 Google Scholar
[25]	KeKelis G J, Zisman M S, Scott D K, et al. 1978 Phys. Rev. C 17 1929 Google Scholar
[26]	Kryger R A, Azhair A, Hellstrom M, et al. 1995 Phys. Rev. Lett. 74 860 Google Scholar
[27]	Suzuki D, Iwasaki H, Beaumel D, et al. 2009 Phys. Rev. Lett. 103 152503 Google Scholar
[28]	Woodward C J, Tribble R E, Tanner D M, et al. 1983 Phys. Rev. C 27 27
[29]	Mukha I, Summerer K, Acosta L, et al. 2007 Phys. Rev. Lett. 99 182501 Google Scholar
[30]	Pfützner M, Karny M, Grigorenko L, et al. 2012 Rev. Mod. Phys. 84 567 Google Scholar
[31]	Blank B, Ploszajczak M 2008 Rep. Prog. Phys. 71 046301 Google Scholar
[32]	Blank B, Borge M J G 2008 Prog. Part. Nucl. Phys. 60 403 Google Scholar
[33]	方德清, 马余刚 2020 科学通报 65 4018 Google Scholar Fang D Q, Ma Y G 2020 Chin. Sci. Bull. 65 4018 Google Scholar
[34]	Fisker J L, Thielemann F K, Wiescher M 2004 Astrophys. J. 608 L61 Google Scholar
[35]	Janecke J 1965 Nucl. Phys. 61 326 Google Scholar
[36]	Brown B A 1991 Phys. Rev. C 43 R1513 Google Scholar
[37]	Galitsky V M, Cheltsov V F 1964 Nucl. Phys. 56 86 Google Scholar
[38]	Nazarewicz W, Dobaczewski J, Werner T R, et al. 1996 Phys. Rev. C 53 740 Google Scholar
[39]	Grigorenko L V, Zhukov M V 2007 Phys. Rev. C 76 014008 Google Scholar
[40]	Delion D S, Liotta R J, Wyss R 2013 Phys. Rev. C 87 034328 Google Scholar
[41]	Liu H M, Pan X, Zou Y T, et al. 2021 Chin. Phys. C 45 044110 Google Scholar
[42]	Sreeja I, Balasubramaniam M 2019 Eur. Phys. J. A 55 33 Google Scholar
[43]	Olsen E, Pfutzner M, Birge N, et al. 2013 Phys. Rev. Lett. 110 222501 Google Scholar
[44]	Kadmensky S G 2005 Phys. At. Nucl. 68 184
[45]	Alvarez-Rodrýguez R, Jensen A S, Garrido E, Fedorov D V 2010 Phys. Rev. C 82 034001 Google Scholar
[46]	Gonalves M, Teruya N, Tavares O, et al. 2017 Phys. Lett. B 774 14 Google Scholar
[47]	Cui J P, Gao Y H, Wang Y Z, Gu J Z 2020 Phys. Rev. C 101 014301
[48]	Wang Y Z, Cui J P, Gao Y H, Gu J Z 2021 Commun. Theor. Phys. 73 075301 Google Scholar
[49]	Wang Y Z, Wang S J, Hou Z Y, Gu J Z 2015 Phys. Rev. C 92 064301
[50]	Wang Y Z, Xing F Z, Xiao Y, Gu J Z 2021 Chin. Phys. C 45 044111 Google Scholar
[51]	Xing F Z, Cui J P, Wang Y Z, Gu J Z 2021 Chin. Phys. C 45 124105 Google Scholar
[52]	Ma Y G, Fang D Q, Sun X Y, et al. 2015 Phys. Lett. B 743 306 Google Scholar
[53]	Fang D Q, Ma Y G, Sun X Y, et al. 2016 Phys. Rev. C 94 044621 Google Scholar
[54]	Lin C J, Xu X X, Jia H M, et al. 2009 Phys. Rev. C 80 014310 Google Scholar
[55]	Mukha I, Roeckl E, Batist L, et al. 2006 Nature 439 298 Google Scholar
[56]	Kankainen A, Elomaa V V, Batist L, et al. 2008 Phys. Rev. Lett. 101 142503 Google Scholar
[57]	Duarte S B, Tavares O A P, Guzman F, et al. 2002 At. Data Nucl. Data Tables 80 235 Google Scholar
[58]	Wang Y Z, Cui J P, Zhang Y L, Zhang S, Gu J Z 2017 Phys. Rev. C 95 014302
[59]	王艳召, 崔建坡, 刘军, 苏学斗 2017 原子能科学技术 51 1544 Google Scholar Wang Y Z, Cui J P, Liu J, Su X D 2017 Atom. Energ. Sci. Technol. 51 1544 Google Scholar
[60]	圣宗强, 舒良萍, 孟影, 胡继刚, 钱建发 2014 物理学报 63 162302 Google Scholar Sheng Z Q, Shu L P, Meng Y, Hu J G, Qian J F 2014 Acta Phys. Sin. 63 162302 Google Scholar
[61]	张小平, 任中洲 2006 高能物理与核物理 30 47 Zhang X P, Ren Z Z 2006 High Energ. Phys. Nucl. Phys. 30 47
[62]	Cui J P, Gao Y H, Wang Y Z, Gu J Z 2022 Nucl. Phys. A 1017 122341 Google Scholar
[63]	Royer G 2000 J. Phys. G Nucl. Part. Phys. 26 1149 Google Scholar
[64]	Mukha I, Roeckl E, Doring J, et al. 2005 Phys. Rev. Lett. 95 022501 Google Scholar
[65]	Pechenaya O L, Chiara C J, Sarantites D G, et al. 2007 Phys. Rev. C 76 011304(R
[66]	Cerny J, Moltz D M, Lee D W, et al. 2009 Phys. Rev. Lett. 103 152502 Google Scholar
[67]	Mukha I, Grawe H, Roeckl E, Tabor S 2008 Phys. Rev. C 78 039803 Google Scholar
[68]	Pechenaya O L, Sarantites D G, Reviol W, Chiara C J, Janssens R V F, Lister C J, Seweryniak D 2008 Phys. Rev. C 78 039804 Google Scholar
[69]	Zerguerras T, Blank B, Blumenfeld Y, et al. 2004 Eur. Phys. J. A 20 389 Google Scholar
[70]	马余刚, 赵红卫 2020 中国科学: 物理学力学天文学 50 112001 Google Scholar Ma Y G, Zhao H W 2020 Sci. Sin. -Phys. Mech. Astron. 50 112001 Google Scholar
[71]	Otsuka T, Suzuki T, Fujimoto R, et al. 2005 Phys. Rev. Lett. 95 232502 Google Scholar
[72]	Holt J D, Menendez J, Schwenk A 2013 Phys. Rev. Lett. 110 022502 Google Scholar
[73]	Qi C, Chen T 2015 Phys. Rev. C 92 051304 Google Scholar

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Vol. 71, Issue 6 - 2022-03-20

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