Liquid Drop Model of Nucleus

核的液滴模型

Scattering experiments suggest that nuclei have approximately constant density, so that the nuclear radius can be calculated by using that density as if the nucleus were a drop of a uniform liquid. A liquid drop model of the nucleus would take into account the fact that the forces on the nucleons on the surface are different from those on nucleons on the interior where they are completely surrounded by other attracting nucleons. This is something similar to taking account of surface tension as a contributor to the energy of a tiny liquid drop. The volume of the liquid drop is proportional to the mass number A, and the surface would then be proportional to the two-thirds power of A.

散射实验表明，核的密度近似恒定，因此可以将核的半径视为一个均匀液体滴的体积，用该密度来计算。一个液滴模型可以考虑核中位于表面的核子所受的力与内部完全被其他吸引核子包围的核子所受的力不同。这类似于考虑表面张力作为小液滴能量的贡献。液滴的体积与质量数A成正比，而表面则与A的三分之一次方成正比。

The first step toward a liquid drop model of the nucleus would then be to postulate a volume term and a surface term in the form:

建立核的液滴模型的第一步则是提出一个体积项和一个表面项，形式为：

This simple model in fact gives a reasonable approximation of the variation of nuclear binding energy with mass number when the constants have the values

这种简单的模型实际上在质量数变化时，当常数取相应值时，能给出合理的近似。

Another contribution to the binding energy would be the coulomb repulsion of the protons, so there should be a negative term proportional to the square of the atomic number Z :

另一个对结合能的贡献是质子之间的库仑排斥，因此应有一个与原子序数Z的平方成正比的负项：

The Pauli principle favors nuclei in which A=2Z, so the empirical model of binding energy contains a term of the form

泡利原理倾向于那些A=2Z的核，因此经验结合能模型中包含一个形式为的项

Discussion of Pauli contribution

对泡利贡献的讨论

The Pauli principle also favors nuclear configurations with even numbers of neutrons and protons. In the liquid drop model, this is included by using the even-odd nucleus as a reference and adding a correction term which is positive for even-even nuclei and negative for odd-odd nuclei. This strategy for modeling the nuclear binding energy is attributed to Weizsaecker and called the Weizsaecker formula.

泡利原理也倾向于偶数中子和质子数的核构型。在液滴模型中，这是通过以偶-奇核作为参考，并添加一个修正项来实现的，该修正项对于偶-偶核为正，对于奇-奇核为负。这种对核结合能建模的策略归因于魏茨泽克，并被称为魏茨泽克公式。

Weizsaecker formula

魏茨泽克公式

Index

Nuclear Structure Concepts

Reference
Rohlf
Sec 11.3

索引核结构概念参考Rohlf第11章第3节

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The Weizsaecker Formula

Weizsaecker 公式

The Weizsaecker formula is an empirically refined form of the liquid drop model for the binding energy of nuclei. It is also referred to as the "semi-empirical mass formula" and the "Bethe-Weizsaecker formula". Expressed in terms of the mass number A and the atomic number Z for an even-odd nucleus, the Weizsaecker formula is

魏茨泽克公式是液滴模型的一种经验修正形式，用于描述核的结合能。它也被称为“半经验质量公式”和“贝特-魏茨泽克公式”。以偶奇核的质量数A和原子序数Z表示时，魏茨泽克公式为

Using the even-odd as a reference, there are then correction terms for even-even and odd-odd nuclei, the even-even groupings of protons and neutrons being favored in stability.

以偶-奇作为参考，偶-偶和奇-奇核素组则有修正项，偶-偶的质子和中子组合在稳定性上更受青睐。

An estimate of nuclear binding energy can then be obtained by first applying the even-odd formula.

核结合能的估算可以通过首先应用偶-奇公式来获得。

For atomic mass number A = , atomic number Z =

对于原子质量数 A = ，原子序数 Z =

中文译文中的待填/计算数值依次对应：1：a 2：z。实际数值以上方原输入框为准。

and neutron number N = , the even-odd energy figure is

以及中子数 N = ，偶-奇能级图是

中文译文中的待填/计算数值依次对应：1：n。实际数值以上方原输入框为准。

E_b^even-odd = MeV

E b even-odd = MeV（专名或术语）

中文译文中的待填/计算数值依次对应：1：eo。实际数值以上方原输入框为准。

Then, if the nucleus is even-even or odd-odd, the appropriate correction can be made.

然后，如果核是偶-偶或奇-奇，可以做出相应的修正。

E_b^even-even = MeV

E b even-even = MeV（专名或术语）

中文译文中的待填/计算数值依次对应：1：ee。实际数值以上方原输入框为准。

E_b^odd-odd = MeV

E b odd-odd = MeV（专名或术语）

中文译文中的待填/计算数值依次对应：1：oo。实际数值以上方原输入框为准。

With the corrections, the estimate of the nuclear binding energy can be made.

修正后，可以估算出核结合能。

= MeV

This binding energy can be checked by comparing it to the experimental nuclear binding energy in the nuclear data table accessible from the periodic table by clicking on the element and following the links.

Liquid drop model

液滴模型

这种结合能可以通过与核数据表中的实验核结合能进行比较来验证，该核数据表可通过点击元素并遵循链接从元素周期表访问。