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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 of 94Ag 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.
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Keywords:
- two-proton radioactivity /
- excited states /
- half-life /
- effective liquid drop model /
- generalized liquid drop model
[1] Goldansky V I 1960 Nucl. Phys. 19 482Google Scholar
[2] Goldansky V I 1961 Nucl. Phys. 27 648Google Scholar
[3] Cable M D, Honkanen J, Parry R F, et al. 1983 Phys. Rev. Lett. 50 404Google 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 146Google Scholar
[6] Borrel V, Jacmart J C, Pougheon F, et al. 1987 Nucl. Phys. A 473 331Google Scholar
[7] Dossat C, Adimi N, Aksouh F, et al. 2007 Nucl. Phys. A 792 18Google Scholar
[8] Bain C R, Woods P J, Coszach R, et al. 1996 Phys. Lett. B 373 35Google Scholar
[9] Chromik M, Brown B A, Fauerbach M, et al. 1997 Phys. Rev. C 55 1676Google Scholar
[10] Chromik M J, Thirolf P G, Thoennessen M, et al. 2002 Phys. Rev. C 66 024313Google Scholar
[11] Gomez del Campo J, Galindo-Uribarri A, Beene J R, et al. 2001 Phys. Rev. Lett. 86 43Google Scholar
[12] Raciti G, Cardella G, De Napoli M, et al. 2008 Phys. Rev. Lett. 100 192503Google Scholar
[13] Goldansky V I 1988 Phys. Lett. B 212 11Google Scholar
[14] Pfützner M, Badura E, Bingham C, et al. 2002 Eur. Phys. J. A 14 279Google Scholar
[15] Giovinazzo J, Blank B, Chartier M, et al. 2002 Phys. Rev. Lett. 89 102501Google Scholar
[16] Dossat C, Bey A, Blank B, et al. 2005 Phys. Rev. C 72 054315Google Scholar
[17] Pomorski M, Pfützner M, Dominik W, et al. 2014 Phys. Rev. C 90 014311Google Scholar
[18] Wang M, Audi G, Kondev F G, et al. 2017 Chin. Phys. C 41 030003Google 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 232501Google Scholar
[21] Ascher P, Audirac L, Adimi N, et al. 2011 Phys. Rev. Lett. 107 102502Google Scholar
[22] Goigoux T, Ascher P, Blank B, et al. 2016 Phys. Rev. Lett. 117 162501Google Scholar
[23] Whaling W 1966 Phys. Rev. C 150 836Google Scholar
[24] Jager M F, Charity R J, Elson J M, et al. 2012 Phys. Rev. C 86 011304Google Scholar
[25] KeKelis G J, Zisman M S, Scott D K, et al. 1978 Phys. Rev. C 17 1929Google Scholar
[26] Kryger R A, Azhair A, Hellstrom M, et al. 1995 Phys. Rev. Lett. 74 860Google Scholar
[27] Suzuki D, Iwasaki H, Beaumel D, et al. 2009 Phys. Rev. Lett. 103 152503Google 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 182501Google Scholar
[30] Pfützner M, Karny M, Grigorenko L, et al. 2012 Rev. Mod. Phys. 84 567Google Scholar
[31] Blank B, Ploszajczak M 2008 Rep. Prog. Phys. 71 046301Google Scholar
[32] Blank B, Borge M J G 2008 Prog. Part. Nucl. Phys. 60 403Google Scholar
[33] 方德清, 马余刚 2020 科学通报 65 4018Google Scholar
Fang D Q, Ma Y G 2020 Chin. Sci. Bull. 65 4018Google Scholar
[34] Fisker J L, Thielemann F K, Wiescher M 2004 Astrophys. J. 608 L61Google Scholar
[35] Janecke J 1965 Nucl. Phys. 61 326Google Scholar
[36] Brown B A 1991 Phys. Rev. C 43 R1513Google Scholar
[37] Galitsky V M, Cheltsov V F 1964 Nucl. Phys. 56 86Google Scholar
[38] Nazarewicz W, Dobaczewski J, Werner T R, et al. 1996 Phys. Rev. C 53 740Google Scholar
[39] Grigorenko L V, Zhukov M V 2007 Phys. Rev. C 76 014008Google Scholar
[40] Delion D S, Liotta R J, Wyss R 2013 Phys. Rev. C 87 034328Google Scholar
[41] Liu H M, Pan X, Zou Y T, et al. 2021 Chin. Phys. C 45 044110Google Scholar
[42] Sreeja I, Balasubramaniam M 2019 Eur. Phys. J. A 55 33Google Scholar
[43] Olsen E, Pfutzner M, Birge N, et al. 2013 Phys. Rev. Lett. 110 222501Google 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 034001Google Scholar
[46] Gonalves M, Teruya N, Tavares O, et al. 2017 Phys. Lett. B 774 14Google 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 075301Google 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 044111Google Scholar
[51] Xing F Z, Cui J P, Wang Y Z, Gu J Z 2021 Chin. Phys. C 45 124105Google Scholar
[52] Ma Y G, Fang D Q, Sun X Y, et al. 2015 Phys. Lett. B 743 306Google Scholar
[53] Fang D Q, Ma Y G, Sun X Y, et al. 2016 Phys. Rev. C 94 044621Google Scholar
[54] Lin C J, Xu X X, Jia H M, et al. 2009 Phys. Rev. C 80 014310Google Scholar
[55] Mukha I, Roeckl E, Batist L, et al. 2006 Nature 439 298Google Scholar
[56] Kankainen A, Elomaa V V, Batist L, et al. 2008 Phys. Rev. Lett. 101 142503Google Scholar
[57] Duarte S B, Tavares O A P, Guzman F, et al. 2002 At. Data Nucl. Data Tables 80 235Google 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 1544Google Scholar
Wang Y Z, Cui J P, Liu J, Su X D 2017 Atom. Energ. Sci. Technol. 51 1544Google Scholar
[60] 圣宗强, 舒良萍, 孟影, 胡继刚, 钱建发 2014 物理学报 63 162302Google Scholar
Sheng Z Q, Shu L P, Meng Y, Hu J G, Qian J F 2014 Acta Phys. Sin. 63 162302Google 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 122341Google Scholar
[63] Royer G 2000 J. Phys. G Nucl. Part. Phys. 26 1149Google Scholar
[64] Mukha I, Roeckl E, Doring J, et al. 2005 Phys. Rev. Lett. 95 022501Google 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 152502Google Scholar
[67] Mukha I, Grawe H, Roeckl E, Tabor S 2008 Phys. Rev. C 78 039803Google 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 039804Google Scholar
[69] Zerguerras T, Blank B, Blumenfeld Y, et al. 2004 Eur. Phys. J. A 20 389Google Scholar
[70] 马余刚, 赵红卫 2020 中国科学: 物理学 力学 天文学 50 112001Google Scholar
Ma Y G, Zhao H W 2020 Sci. Sin. -Phys. Mech. Astron. 50 112001Google Scholar
[71] Otsuka T, Suzuki T, Fujimoto R, et al. 2005 Phys. Rev. Lett. 95 232502Google Scholar
[72] Holt J D, Menendez J, Schwenk A 2013 Phys. Rev. Lett. 110 022502Google Scholar
[73] Qi C, Chen T 2015 Phys. Rev. C 92 051304Google Scholar
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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 QExp./MeV ${\lg}{T_{1/2} }/{\text{s} }$ 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 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 — 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 -
[1] Goldansky V I 1960 Nucl. Phys. 19 482Google Scholar
[2] Goldansky V I 1961 Nucl. Phys. 27 648Google Scholar
[3] Cable M D, Honkanen J, Parry R F, et al. 1983 Phys. Rev. Lett. 50 404Google 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 146Google Scholar
[6] Borrel V, Jacmart J C, Pougheon F, et al. 1987 Nucl. Phys. A 473 331Google Scholar
[7] Dossat C, Adimi N, Aksouh F, et al. 2007 Nucl. Phys. A 792 18Google Scholar
[8] Bain C R, Woods P J, Coszach R, et al. 1996 Phys. Lett. B 373 35Google Scholar
[9] Chromik M, Brown B A, Fauerbach M, et al. 1997 Phys. Rev. C 55 1676Google Scholar
[10] Chromik M J, Thirolf P G, Thoennessen M, et al. 2002 Phys. Rev. C 66 024313Google Scholar
[11] Gomez del Campo J, Galindo-Uribarri A, Beene J R, et al. 2001 Phys. Rev. Lett. 86 43Google Scholar
[12] Raciti G, Cardella G, De Napoli M, et al. 2008 Phys. Rev. Lett. 100 192503Google Scholar
[13] Goldansky V I 1988 Phys. Lett. B 212 11Google Scholar
[14] Pfützner M, Badura E, Bingham C, et al. 2002 Eur. Phys. J. A 14 279Google Scholar
[15] Giovinazzo J, Blank B, Chartier M, et al. 2002 Phys. Rev. Lett. 89 102501Google Scholar
[16] Dossat C, Bey A, Blank B, et al. 2005 Phys. Rev. C 72 054315Google Scholar
[17] Pomorski M, Pfützner M, Dominik W, et al. 2014 Phys. Rev. C 90 014311Google Scholar
[18] Wang M, Audi G, Kondev F G, et al. 2017 Chin. Phys. C 41 030003Google 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 232501Google Scholar
[21] Ascher P, Audirac L, Adimi N, et al. 2011 Phys. Rev. Lett. 107 102502Google Scholar
[22] Goigoux T, Ascher P, Blank B, et al. 2016 Phys. Rev. Lett. 117 162501Google Scholar
[23] Whaling W 1966 Phys. Rev. C 150 836Google Scholar
[24] Jager M F, Charity R J, Elson J M, et al. 2012 Phys. Rev. C 86 011304Google Scholar
[25] KeKelis G J, Zisman M S, Scott D K, et al. 1978 Phys. Rev. C 17 1929Google Scholar
[26] Kryger R A, Azhair A, Hellstrom M, et al. 1995 Phys. Rev. Lett. 74 860Google Scholar
[27] Suzuki D, Iwasaki H, Beaumel D, et al. 2009 Phys. Rev. Lett. 103 152503Google 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 182501Google Scholar
[30] Pfützner M, Karny M, Grigorenko L, et al. 2012 Rev. Mod. Phys. 84 567Google Scholar
[31] Blank B, Ploszajczak M 2008 Rep. Prog. Phys. 71 046301Google Scholar
[32] Blank B, Borge M J G 2008 Prog. Part. Nucl. Phys. 60 403Google Scholar
[33] 方德清, 马余刚 2020 科学通报 65 4018Google Scholar
Fang D Q, Ma Y G 2020 Chin. Sci. Bull. 65 4018Google Scholar
[34] Fisker J L, Thielemann F K, Wiescher M 2004 Astrophys. J. 608 L61Google Scholar
[35] Janecke J 1965 Nucl. Phys. 61 326Google Scholar
[36] Brown B A 1991 Phys. Rev. C 43 R1513Google Scholar
[37] Galitsky V M, Cheltsov V F 1964 Nucl. Phys. 56 86Google Scholar
[38] Nazarewicz W, Dobaczewski J, Werner T R, et al. 1996 Phys. Rev. C 53 740Google Scholar
[39] Grigorenko L V, Zhukov M V 2007 Phys. Rev. C 76 014008Google Scholar
[40] Delion D S, Liotta R J, Wyss R 2013 Phys. Rev. C 87 034328Google Scholar
[41] Liu H M, Pan X, Zou Y T, et al. 2021 Chin. Phys. C 45 044110Google Scholar
[42] Sreeja I, Balasubramaniam M 2019 Eur. Phys. J. A 55 33Google Scholar
[43] Olsen E, Pfutzner M, Birge N, et al. 2013 Phys. Rev. Lett. 110 222501Google 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 034001Google Scholar
[46] Gonalves M, Teruya N, Tavares O, et al. 2017 Phys. Lett. B 774 14Google 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 075301Google 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 044111Google Scholar
[51] Xing F Z, Cui J P, Wang Y Z, Gu J Z 2021 Chin. Phys. C 45 124105Google Scholar
[52] Ma Y G, Fang D Q, Sun X Y, et al. 2015 Phys. Lett. B 743 306Google Scholar
[53] Fang D Q, Ma Y G, Sun X Y, et al. 2016 Phys. Rev. C 94 044621Google Scholar
[54] Lin C J, Xu X X, Jia H M, et al. 2009 Phys. Rev. C 80 014310Google Scholar
[55] Mukha I, Roeckl E, Batist L, et al. 2006 Nature 439 298Google Scholar
[56] Kankainen A, Elomaa V V, Batist L, et al. 2008 Phys. Rev. Lett. 101 142503Google Scholar
[57] Duarte S B, Tavares O A P, Guzman F, et al. 2002 At. Data Nucl. Data Tables 80 235Google 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 1544Google Scholar
Wang Y Z, Cui J P, Liu J, Su X D 2017 Atom. Energ. Sci. Technol. 51 1544Google Scholar
[60] 圣宗强, 舒良萍, 孟影, 胡继刚, 钱建发 2014 物理学报 63 162302Google Scholar
Sheng Z Q, Shu L P, Meng Y, Hu J G, Qian J F 2014 Acta Phys. Sin. 63 162302Google 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 122341Google Scholar
[63] Royer G 2000 J. Phys. G Nucl. Part. Phys. 26 1149Google Scholar
[64] Mukha I, Roeckl E, Doring J, et al. 2005 Phys. Rev. Lett. 95 022501Google 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 152502Google Scholar
[67] Mukha I, Grawe H, Roeckl E, Tabor S 2008 Phys. Rev. C 78 039803Google 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 039804Google Scholar
[69] Zerguerras T, Blank B, Blumenfeld Y, et al. 2004 Eur. Phys. J. A 20 389Google Scholar
[70] 马余刚, 赵红卫 2020 中国科学: 物理学 力学 天文学 50 112001Google Scholar
Ma Y G, Zhao H W 2020 Sci. Sin. -Phys. Mech. Astron. 50 112001Google Scholar
[71] Otsuka T, Suzuki T, Fujimoto R, et al. 2005 Phys. Rev. Lett. 95 232502Google Scholar
[72] Holt J D, Menendez J, Schwenk A 2013 Phys. Rev. Lett. 110 022502Google Scholar
[73] Qi C, Chen T 2015 Phys. Rev. C 92 051304Google Scholar
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