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Neutron-excessive nuclei and two-proton radioactivity
Volume 212, n u m b e r 1
PHYSICS LETTERS B
15 September 1988
NEUTRON-EXCESSIVE N U C L E I AND T W O - P R O T O N RADIOACTIVITY Vitalii I. GOLDANSKII Institute of Chemical Physics, Academy of Sciences of the USSR, Ulitsa Kosygina 4, Moscow I 17334, USSR Received 19 May 1988
New experimental data on nuclei with large neutron excess, combined with an earlier formula which connected binding energies of neutrons in such nuclei with those of protons in mirror neutron-deficient nuclei, give quite reliable predictions of the properties of four isotopes which are expected to manifest two-proton radioactivity, 22Si, 3~Ar, 39Ti and 42Cr.
Already 28 years have passed since the predicted existence and description of the expected properties of the fifth main type of radioactive decay of nuclei two-proton radioactivity [ 1-3 ]. However, such decay of ground state nuclei has not yet been observed, and up to now only beta-delayed emission of two protons has been detected [ 4-7 ]. In this connection it would be of certain interest to outline more precisely the region of virtual 2p radioactive nuclei in view of much recent experimental data [ 8 ] on the binding energies of pairs of neutrons in the neutron-rich isotopes of light elements (from beryllium to scandium) - see fig. 1. In accordance with our formulae [ 1,2 ] based on the isotopic invariance of nuclear forces, the binding energy of a pair of protons S2o in the nucleus (A, Z) of Z protons and N = A - Z neutrons is connected to the binding energy of a pair of neutrons $2, in the mirror nucleus (A, A - Z) by a very simple relation:
Fig. 1 represents the totality of data of ref. [ 8 ] on the binding energies of pairs of neutrons S2n in the
> .-7 CO
g~ CO
S2n(A, A - Z ) -S2p(A, Z ) = AB2.,2p = ABo + AB~ = S , (2Z, Z)-Sp(2Z, Z ) + S , ( 2 Z - 2 , Z - 1)
-Sp(2Z-Z,Z-1) ,
(1)
where ABo and AB3 are the differences in neutron and proton binding energies in isotopically self-conjugate nuclei which contain equal ( Z or Z - 1 each) numbers of protons and neutrons. Comparative analysis [ 9 ] of different predictions of atomic masses shows that the formulae of type ( I ) give more reliable values of masses and decay energies of neutron deficient nuclei than the well-known Garvey-Kelson formulae [ 10 ], with the accuracy of the predictions of formula ( 1 ) no worse than 100 keV. 0370-2693/88/$ 03.50 © Elsevier Science Publishers B.V. ( North-Holland Physics Publishing Division )
8
I0 12 14 16 18 20 22 24 Na AI P Cl K Sc V Mn Ne Mg Si S Ar Ca Ti Cr N (Z) Fig. l. The data on binding energies of pairs of neutrons ($2,) are plotted, as in ref. [8], as a function of neutron number. If neutron n u m b e r (N) and proton n u m b e r (Z) were interchanged, the curve labelled "ABo + ABe" gives the estimate of the difference between the magnitudes of $2, and S2p, so that the points below this curve correspond to isotopes that may be expected to be unstable against 2p emission. N
F
0
II
Volume 212, number 1
15 September 1988
PHYSICS LETTERS B
Table 1 Expected characteristics of decay of 2p-radioactive isotopes.
Qzp (MeV) Zzp (s) E~+ max (MeV) E ~ + ( A T = 0 ) (MeV) E * ( A T = 0 ) (MeV) %+ ( A T = 0 ) (s) chain of decays after [3+ (AT=O)
225i
3~Ar
39Ti
42Cr
0.15 102 14.4 3.8 10.6 2.0
0.25 104 15.9 5.3 10.6 0.5
0.75 10 -5 15.3 6.2 9.1 0.3
0.4 104 13.4 6.7 6.7 0.2
[3+pp
[3+pp
13+pp
[3+pp
(neutron rich) isotopes of eighteen elements ( Z = 4 21). The line rising from left to right presents the values of/~kB2n,2 p = A n 0 -~-/~kB~ and is based mainly on experimental data from the atomic mass tables [ 11 ]. Clearly, the position of S2n points below the ABzn,2o curve corresponds to the negative binding energy of pairs of protons in the isotopes of even elements, which are shown at the abscissa, and neutron numbers are equal to the nuclear charges at the initial experimental curves S2n (ref. [ 8 ] ). Let us give one numerical example. The value of S2n for the neutron-rich isotope 220~4 equals 10.5 MeV (ref. [8]), and the s u m AB0(~485i14)+ t 26 ABo(t3All3)10.65 MeV. Thus, although the isotope 22Sis has a slightly negative binding energy for the pair of protons (ca. 0.15 MeV), it still must be perceived as a stable (or almost stable) nuclide versus two-proton decay, i.e., a [3+ emitting isotope - in agreement with recent data [ 12 ]. Altogether, one may expect nine frontier (2p-unstable) isotopes between oxygen and chromium: 120, 16Ne, ~9Mg, 265, 31Ar, 34Ca, 39Ti, 42Cr (not to mention even more unstable, very short-lived neighbours of these nine, e.g., 3°Ar, 38Ti, etc. ). Taking z= 10 -~2 s as an arbitrary lower value of the lifetime of radioactive nuclei (to separate them from conventional particle-unstable nuclei) one can possibly observe two-proton radioactivity for the following four isotopes (see table 1 ): 22Si, 3tAr, 39Ti, and 42Cr. Finally, some short remarks and comments with regard to table 1. Because of the very strong dependence ofz2o on the 2p-decay energy Q2p, the values of r2o should be treated as crude estimates. Besides the total (max) kinetic energy of the positrons for 1]+decay (fourth line) the values of E ~ + ( A T = 0 ) = 12
1 . 2 ( Z - 1 ) / h 1/3- 1.8 MeV are given, which correspond to superallowed 13+-transition (without change of isospin). Lifetimes for such transitions (seventh line) are estimated for logfi = 3.5. Since the daughter nucleus at the superaUowed 13+-transition is strongly excited [by the energy E* ( A T = 0) given in the sixth line ], one also has the possibility of a chain of decays with the subsequent emission of two protons (certainly unpaired - see the cases of 22A1 and 26p refs. [5,6] ) after the 13+-decay. This circumstance should be taken into account in the identification of decay with the emission of two protons, as true two-proton radioactivity. The four isotopes listed in table 1 hardly include all possibilities for the observation of two-proton radioactivity. Among the heavier 2p-active nuclei one can expect to find 55Zn, 59Ge, mSXe, but more detailed analysis requires the data on binding energies of pairs of neutrons in neutron-rich isotopes - so that calculations similar to those performed above for the data of the nuclides from beryllium to scandium [ 8 ], can be carried out. References [ 1 ] V.I. Goldanskii, JETP 12 ( 1961 ) 348. [2] V.I. Goldanskii, Nucl. Phys. 19 (1960) 482. [3] V.I. Goldanskii, Sov. Phys. Usp. 8 (1966) 770. [4] V.I. Goldanskii, JETP Lett. 32 (1980) 554. [ 5 ] M.D. Cable et al., Phys. Rev. Lett. 50 ( 1983 ) 404. [6] M.D. Cable et al., Phys. Lett. B 123 (1983) 25. [7] V.I. Goldanskii, Sov. Phys. Usp. 26 (1983 ). [ 8 ] A. Gillibert et al., Phys. Lett. B 192 ( 1987 ) 39. [9] V.I. Goldanskii, Nucl. Phys. A 133 (1969) 438. [ 10] G.T. Garvey and I. Kelson, Phys. Rev. Len. 16 (1966) 197. [ 11 ] A.H. Wapstra and K. Bos, At. Data Nucl. Data Tables 17 (1975) 474. [12] M.G. Saint-Laurent, Phys. Rev. Lett. 59 (1987) 33.
PHYSICS LETTERS B
15 September 1988
NEUTRON-EXCESSIVE N U C L E I AND T W O - P R O T O N RADIOACTIVITY Vitalii I. GOLDANSKII Institute of Chemical Physics, Academy of Sciences of the USSR, Ulitsa Kosygina 4, Moscow I 17334, USSR Received 19 May 1988
New experimental data on nuclei with large neutron excess, combined with an earlier formula which connected binding energies of neutrons in such nuclei with those of protons in mirror neutron-deficient nuclei, give quite reliable predictions of the properties of four isotopes which are expected to manifest two-proton radioactivity, 22Si, 3~Ar, 39Ti and 42Cr.
Already 28 years have passed since the predicted existence and description of the expected properties of the fifth main type of radioactive decay of nuclei two-proton radioactivity [ 1-3 ]. However, such decay of ground state nuclei has not yet been observed, and up to now only beta-delayed emission of two protons has been detected [ 4-7 ]. In this connection it would be of certain interest to outline more precisely the region of virtual 2p radioactive nuclei in view of much recent experimental data [ 8 ] on the binding energies of pairs of neutrons in the neutron-rich isotopes of light elements (from beryllium to scandium) - see fig. 1. In accordance with our formulae [ 1,2 ] based on the isotopic invariance of nuclear forces, the binding energy of a pair of protons S2o in the nucleus (A, Z) of Z protons and N = A - Z neutrons is connected to the binding energy of a pair of neutrons $2, in the mirror nucleus (A, A - Z) by a very simple relation:
Fig. 1 represents the totality of data of ref. [ 8 ] on the binding energies of pairs of neutrons S2n in the
> .-7 CO
g~ CO
S2n(A, A - Z ) -S2p(A, Z ) = AB2.,2p = ABo + AB~ = S , (2Z, Z)-Sp(2Z, Z ) + S , ( 2 Z - 2 , Z - 1)
-Sp(2Z-Z,Z-1) ,
(1)
where ABo and AB3 are the differences in neutron and proton binding energies in isotopically self-conjugate nuclei which contain equal ( Z or Z - 1 each) numbers of protons and neutrons. Comparative analysis [ 9 ] of different predictions of atomic masses shows that the formulae of type ( I ) give more reliable values of masses and decay energies of neutron deficient nuclei than the well-known Garvey-Kelson formulae [ 10 ], with the accuracy of the predictions of formula ( 1 ) no worse than 100 keV. 0370-2693/88/$ 03.50 © Elsevier Science Publishers B.V. ( North-Holland Physics Publishing Division )
8
I0 12 14 16 18 20 22 24 Na AI P Cl K Sc V Mn Ne Mg Si S Ar Ca Ti Cr N (Z) Fig. l. The data on binding energies of pairs of neutrons ($2,) are plotted, as in ref. [8], as a function of neutron number. If neutron n u m b e r (N) and proton n u m b e r (Z) were interchanged, the curve labelled "ABo + ABe" gives the estimate of the difference between the magnitudes of $2, and S2p, so that the points below this curve correspond to isotopes that may be expected to be unstable against 2p emission. N
F
0
II
Volume 212, number 1
15 September 1988
PHYSICS LETTERS B
Table 1 Expected characteristics of decay of 2p-radioactive isotopes.
Qzp (MeV) Zzp (s) E~+ max (MeV) E ~ + ( A T = 0 ) (MeV) E * ( A T = 0 ) (MeV) %+ ( A T = 0 ) (s) chain of decays after [3+ (AT=O)
225i
3~Ar
39Ti
42Cr
0.15 102 14.4 3.8 10.6 2.0
0.25 104 15.9 5.3 10.6 0.5
0.75 10 -5 15.3 6.2 9.1 0.3
0.4 104 13.4 6.7 6.7 0.2
[3+pp
[3+pp
13+pp
[3+pp
(neutron rich) isotopes of eighteen elements ( Z = 4 21). The line rising from left to right presents the values of/~kB2n,2 p = A n 0 -~-/~kB~ and is based mainly on experimental data from the atomic mass tables [ 11 ]. Clearly, the position of S2n points below the ABzn,2o curve corresponds to the negative binding energy of pairs of protons in the isotopes of even elements, which are shown at the abscissa, and neutron numbers are equal to the nuclear charges at the initial experimental curves S2n (ref. [ 8 ] ). Let us give one numerical example. The value of S2n for the neutron-rich isotope 220~4 equals 10.5 MeV (ref. [8]), and the s u m AB0(~485i14)+ t 26 ABo(t3All3)10.65 MeV. Thus, although the isotope 22Sis has a slightly negative binding energy for the pair of protons (ca. 0.15 MeV), it still must be perceived as a stable (or almost stable) nuclide versus two-proton decay, i.e., a [3+ emitting isotope - in agreement with recent data [ 12 ]. Altogether, one may expect nine frontier (2p-unstable) isotopes between oxygen and chromium: 120, 16Ne, ~9Mg, 265, 31Ar, 34Ca, 39Ti, 42Cr (not to mention even more unstable, very short-lived neighbours of these nine, e.g., 3°Ar, 38Ti, etc. ). Taking z= 10 -~2 s as an arbitrary lower value of the lifetime of radioactive nuclei (to separate them from conventional particle-unstable nuclei) one can possibly observe two-proton radioactivity for the following four isotopes (see table 1 ): 22Si, 3tAr, 39Ti, and 42Cr. Finally, some short remarks and comments with regard to table 1. Because of the very strong dependence ofz2o on the 2p-decay energy Q2p, the values of r2o should be treated as crude estimates. Besides the total (max) kinetic energy of the positrons for 1]+decay (fourth line) the values of E ~ + ( A T = 0 ) = 12
1 . 2 ( Z - 1 ) / h 1/3- 1.8 MeV are given, which correspond to superallowed 13+-transition (without change of isospin). Lifetimes for such transitions (seventh line) are estimated for logfi = 3.5. Since the daughter nucleus at the superaUowed 13+-transition is strongly excited [by the energy E* ( A T = 0) given in the sixth line ], one also has the possibility of a chain of decays with the subsequent emission of two protons (certainly unpaired - see the cases of 22A1 and 26p refs. [5,6] ) after the 13+-decay. This circumstance should be taken into account in the identification of decay with the emission of two protons, as true two-proton radioactivity. The four isotopes listed in table 1 hardly include all possibilities for the observation of two-proton radioactivity. Among the heavier 2p-active nuclei one can expect to find 55Zn, 59Ge, mSXe, but more detailed analysis requires the data on binding energies of pairs of neutrons in neutron-rich isotopes - so that calculations similar to those performed above for the data of the nuclides from beryllium to scandium [ 8 ], can be carried out. References [ 1 ] V.I. Goldanskii, JETP 12 ( 1961 ) 348. [2] V.I. Goldanskii, Nucl. Phys. 19 (1960) 482. [3] V.I. Goldanskii, Sov. Phys. Usp. 8 (1966) 770. [4] V.I. Goldanskii, JETP Lett. 32 (1980) 554. [ 5 ] M.D. Cable et al., Phys. Rev. Lett. 50 ( 1983 ) 404. [6] M.D. Cable et al., Phys. Lett. B 123 (1983) 25. [7] V.I. Goldanskii, Sov. Phys. Usp. 26 (1983 ). [ 8 ] A. Gillibert et al., Phys. Lett. B 192 ( 1987 ) 39. [9] V.I. Goldanskii, Nucl. Phys. A 133 (1969) 438. [ 10] G.T. Garvey and I. Kelson, Phys. Rev. Len. 16 (1966) 197. [ 11 ] A.H. Wapstra and K. Bos, At. Data Nucl. Data Tables 17 (1975) 474. [12] M.G. Saint-Laurent, Phys. Rev. Lett. 59 (1987) 33.