Erratum and Addendum: Empirical pairing gaps and neutron-proton correlations (Chin. Phys. C, 43(1): 014104 (2019))

Get Citation
B. S. Ishkhanov, S. V. Sidorov, T. Yu. Tretyakova and E. V. Vladimirova. Erratum and Addendum: Empirical pairing gaps and neutron-proton correlations (Chin. Phys. C, 43(1): 014104 (2019))[J]. Chinese Physics C. doi: 10.1088/1674-1137/44/6/069102
B. S. Ishkhanov, S. V. Sidorov, T. Yu. Tretyakova and E. V. Vladimirova. Erratum and Addendum: Empirical pairing gaps and neutron-proton correlations (Chin. Phys. C, 43(1): 014104 (2019))[J]. Chinese Physics C.  doi: 10.1088/1674-1137/44/6/069102 shu
Milestone
Received: 2018-07-18
Revised: 2018-10-08
Article Metric

Article Views(776)
PDF Downloads(25)
Cited by(0)
Policy on re-use
To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.
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

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Email This Article

Title:
Email:

Erratum and Addendum: Empirical pairing gaps and neutron-proton correlations (Chin. Phys. C, 43(1): 014104 (2019))

    Corresponding author: T. Yu. Tretyakova, tretyakova@sinp.msu.ru
  • 1. Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia
  • 2. Skobeltzyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991, Russia

Abstract: 

    HTML

  • In our article we wrote the three-point mass relation based on deutron separation energies in the form

    $ \begin{split} \Delta_{np}^{(3)}(N,Z) =& \frac{(-1)^{N+1}}{2}\left(S_d(N+1, Z+1) - S_d(N,Z)\right) \\ =& \frac{(-1)^{N+1}}{2}\left(B(N+1,Z+1)-\right.\\ & \left.- 2B(N,Z)+B(N-1,Z-1)\right), \end{split}$

    (1)

    which holds true for the case of even-A nuclei. Factor $ (-1)^{N+1} $ is taken into account to reproduce the even-odd staggering (EOS) effect for even-even and odd-odd nuclei. For the case of odd-A nuclei, on the other hand, the value of $ \Delta_{np}^{(3)}(N,Z) $ was shown to oscillate near the zero value (which corresponds to EOS for odd-even and even-odd nuclei), and taking the corresponding factor into account makes no sense. The corresponding formula (39) for the case when the factor is ommited from odd-A nuclei, should properly read

    $ \begin{split} \Delta _{np}^{(3)}(N,Z) =& \\ = &\frac{1}{2}\left\{ {\begin{array}{*{20}{l}} {({\pi _n} - {d_n}) + ({\pi _p} - {d_p}) - 2(I' + {I^0}),}&{ee}\\ {({\pi _n} + {d_n}) + ( - {\pi _p} + {d_p}) + 2{I^0},}&{oe}\\ {( - {\pi _n} + {d_n}) + ({\pi _p} + {d_p}) + 2{I^0},}&{eo}\\ {({\pi _n} + {d_n}) + ({\pi _p} + {d_p}) - 2(I' - {I^0}),}&{oo} \end{array}} \right. \end{split} $

    (2)

    As a result, for the case of odd-A nuclei factor $ (-1)^{N+1} $ leads to the change of general sign for even-N nuclei:

    $ \begin{split} \Delta_{np}^{(3)}(N,Z) =& \frac{(-1)^{N+1}}{2}\left(S_d(N+1, Z+1) - S_d(N,Z)\right) \\=&-\frac12\left((-\pi_n + d_n)+(\pi_p + d_p)+2I^0\right), \end{split} $

    (3)

    The inclusion of factor $ (-1)^{N+1} $ for odd-A nuclei significantly affects the $ \Delta_{np}^{(4)} $, resulting from the averaging of $ \Delta_{np}^{(3)}(N,Z) $. Instead of expression (40) we get:

    $ \Delta _{np}^{(4)}(N,Z) = \frac{1}{2}\left\{ {\begin{array}{*{20}{l}} {\left( {{\pi _n} + {\pi _p}} \right) - 2I',}&{ee,oo}\\ {{\pi _n} - {\pi _p},}&{oe,eo} \end{array}} \right. $

    (4)

    Since, as noted above, we are talking about values close to zero, the noted changes do not affect the main conclusions of the article. However, the ratio in Eq. (42)

    $ \pi_p \approx \pi_n $

    is approximate and, as can be seen from Table 2, the values of $ \pi_p $ consistently exceed the values of $ \pi_n $. From this point of view, the choice of the factor $ (-1)^{Z+1} $ used in the expression coinciding with $ \Delta_{np}^{(4)} $ in [1] is more reasonable.

    One more remark concerns the formulas for $ \Delta_{np}^{MN} $ first introduced in [2]. In formula (19), the proper factor should be $ (-1)^{A+1} $. In (20), the two cases correspond to even and odd values of Z rather than N, while in (21), vice versa, these are the cases of even and odd N rather than Z.

Reference (2)

目录

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return