B(E2) values in T=1 multiplets and isospin purity

P.D. Cottle

In nuclear structure physics, isospin is a powerful symmetry that provides critical insights regarding the complex proton-neutron system. Bernstein, Brown and Madsen [1] pointed out that electromagnetic transition rates in T=1 multiplets can be used to test isospin purity. In the convention given by Bernstein, Brown and Madsen, the proton multipole transition matrix element,

M_p = (1/e)[B(E2; 0⁺® 2⁺)]^1/2,

is written in the isospin representation as

M_p(T_z) = (1/2)[M₀(T_z) – M₁(T_z)],

where M₀(T_z) and M₁(T_z) are the isoscalar and isovector multipole matrix elements, respectively. The assumption of isospin conservation gives the relationships between matrix elements in different isobars

M₀(T_z’)= M₀(T_z)

M₀(T_z’)= M₀(T_z)T_z’/T_z.

If two nuclei are mirrors, then T_z’=-T_z and

M₀(T_z) =M_p(T_z) + M_p(-T_z)

Equation (6) also implies that for the corresponding transition between $T=1$ states in a $T_z=0$ nucleus

M_p(T_z=0)= M₀(T_z=1)/2.

If the isospin symmetry holds, then the isoscalar multipole matrix element M₀ given by the transitions in the T_z=±1isobars is equal to the corresponding matrix element given by the T_z=0 isobar.

A comparison of the M₀ values from T_z=±1and T_z=0 isobars for A=4n+2 T=1 isospin multiplets for masses up to 42 was published in 1999 as part of a study of the intermediate energy Coulomb excitation of ³⁸Ca [2]. A number of experiments since then have provided updated values of M₀in these multiplets [3-6]. In addition, compilations [7,8] have been updated as well. Figure 1 reflects these updates. It is worth noting that a careful analysis of the trends observed in these multiplets using the shell model was described in [9].

In comparing the present figure with the corresponding one from 1999 (Ref. 2), it can be seen that the discrepancies that arose between M₀ values from the T_z=±1and T_z=0 isobars in the A=34 and A=42 multiplets in the 1999 plot have been resolved. The discrepancy identified in the A=38 system at that time remains. However, Prados Estevez et al. [6] argued on the basis of their remeasurement of the applicable transition in ³⁸K and shell model calculations that the member of the A=38 multiplet that appears most anomalous (when compared to their shell model calculations) is ³⁸Ca, for which the B(E2) matrix element has been measured via intermediate energy Coulomb excitation [2]. This situation clearly requires a reexamination of ³⁸Ca.

[1] A.M. Bernstein, V.R. Brown and V.A. Madsen, Phys. Rev. Lett. 42, 425 (1979).

[2] P.D. Cottle et al., Phys. Rev. C 60, 031301(R) (1999).

[3] P.D. Cottle et al., Phys. Rev. C 64, 057304 (2001).

[4] L.A. Riley et al., Phys. Rev. C 68, 044309 (2003).

[4] S. Schielke et al., Phys. Lett. B 571, 29 (2003).

[5] J.N. Orce et al., Phys. Rev. C 70, 014314 (2004).

[6] F.M. Prados Estevez et al., Phys. Rev. C 75, 014309 (2007).

[7] Evaluated Nuclear Structure Data File (ENSDF), National Nuclear Data Center (http://www.nndc.bnl.gov).

[8] S. Raman, C.W. Nestor, Jr., and P. Tikkanen, At. Data Nucl. Data Tables 78, 1 (2001).

[9] J.N. Orce and V. Velazquez, Nucl. Phys. A 764, 205 (2006).

Figure 1

Comparison of M₀ values extracted from comparisons of M_pfor 0_gs⁺® 2₁⁺ transitions in T_z=±1 to the M₀ values taken from 0_T=1⁺® 2_T=1⁺ transitions in T_z=0 nuclei. Data are updated through summer 2007 as described in the text.




	FSU Experimental Nuclear Physics Main			*B(E2) values in T=1 multiplets and isospin purity* *P.D. Cottle* In nuclear structure physics, isospin is a powerful symmetry that provides critical insights regarding the complex proton-neutron system. Bernstein, Brown and Madsen [1] pointed out that electromagnetic transition rates in T=1 multiplets can be used to test isospin purity. In the convention given by Bernstein, Brown and Madsen, the proton multipole transition matrix element, M_p = (1/e)[B(E2; 0⁺® 2⁺)]^1/2, is written in the isospin representation as M_p(T_z) = (1/2)[M₀(T_z) – M₁(T_z)], where M₀(T_z) and M₁(T_z) are the isoscalar and isovector multipole matrix elements, respectively. The assumption of isospin conservation gives the relationships between matrix elements in different isobars M₀(T_z’)= M₀(T_z) M₀(T_z’)= M₀(T_z)T_z’/T_z. If two nuclei are mirrors, then T_z’=-T_z and M₀(T_z) =M_p(T_z) + M_p(-T_z) Equation (6) also implies that for the corresponding transition between $T=1$ states in a $T_z=0$ nucleus M_p(T_z=0)= M₀(T_z=1)/2. If the isospin symmetry holds, then the isoscalar multipole matrix element M₀ given by the transitions in the T_z=±1isobars is equal to the corresponding matrix element given by the T_z=0 isobar. A comparison of the M₀ values from T_z=±1and T_z=0 isobars for A=4n+2 T=1 isospin multiplets for masses up to 42 was published in 1999 as part of a study of the intermediate energy Coulomb excitation of ³⁸Ca [2]. A number of experiments since then have provided updated values of M₀in these multiplets [3-6]. In addition, compilations [7,8] have been updated as well. Figure 1 reflects these updates. It is worth noting that a careful analysis of the trends observed in these multiplets using the shell model was described in [9]. In comparing the present figure with the corresponding one from 1999 (Ref. 2), it can be seen that the discrepancies that arose between M₀ values from the T_z=±1and T_z=0 isobars in the A=34 and A=42 multiplets in the 1999 plot have been resolved. The discrepancy identified in the A=38 system at that time remains. However, Prados Estevez et al. [6] argued on the basis of their remeasurement of the applicable transition in ³⁸K and shell model calculations that the member of the A=38 multiplet that appears most anomalous (when compared to their shell model calculations) is ³⁸Ca, for which the B(E2) matrix element has been measured via intermediate energy Coulomb excitation [2]. This situation clearly requires a reexamination of ³⁸Ca. [1] A.M. Bernstein, V.R. Brown and V.A. Madsen, Phys. Rev. Lett. 42, 425 (1979). [2] P.D. Cottle et al., Phys. Rev. C 60, 031301(R) (1999). [3] P.D. Cottle et al., Phys. Rev. C 64, 057304 (2001). [4] L.A. Riley et al., Phys. Rev. C 68, 044309 (2003). [4] S. Schielke et al., Phys. Lett. B 571, 29 (2003). [5] J.N. Orce et al., Phys. Rev. C 70, 014314 (2004). [6] F.M. Prados Estevez et al., Phys. Rev. C 75, 014309 (2007). [7] Evaluated Nuclear Structure Data File (ENSDF), National Nuclear Data Center (http://www.nndc.bnl.gov). [8] S. Raman, C.W. Nestor, Jr., and P. Tikkanen, At. Data Nucl. Data Tables 78, 1 (2001). [9] J.N. Orce and V. Velazquez, Nucl. Phys. A 764, 205 (2006). Figure 1 Comparison of M₀ values extracted from comparisons of M_pfor 0_gs⁺® 2₁⁺ transitions in T_z=±1 to the M₀ values taken from 0_T=1⁺® 2_T=1⁺ transitions in T_z=0 nuclei. Data are updated through summer 2007 as described in the text. Back to Dr. Cottle's Research Menu