Nuclear Size (English)

2-2: Size of Nuclei

[Measurement of Size of Nuclei]

It had already been

known from the analyses with

the Ratherford atomic model

that the nuclear size is

smaller than

roughly speaking.

How can we more precisely measure

the size of individual nucleus?

When we intend to measure

the size of an object,

we irradiate light on the object

and observe the reflected light.

The reflection occurs because of

the interaction between

the light and object.

Similarly,

in order to measure

the nuclear radius,

it appears convenient

to bombard some kinds of particles

to the nucleus

and observe their reaction.

For this purpose,

alpha particles,

nucleons,

electrons,

photons etc.

could be candidates

as projectiles.

Among them, electrons must be

the most convenient.

Electrons can interact

with protons because

they are both electrically

charged.

But electrons do not so strongly

interact with neutron,

so that the reflection of

electrons, i.e. electron scattering,

can be used only for the measurement

of the charge distribution

(or the proton distribution)

in a nucleus.

The proton distribution

in a nucleus may not always

be equal to the mass distribution

including both of

protons and neutrons.

However it would be possible

to get a rough estimation

of the nuclear mass distribution

and the nuclear radius.

This type of precise

measurements have been carried out

and a lot of detailed data

of the nuclear charge distribution

for various nuclei

have been obtained.

A part is shown in

the following figure.

[Experimental Data of Nuclear Charge Distributions]

The data obtained

by the electron scattering.

As an example, the

red curve

shows the proton distribution

in Ca

whose radius is shown by

R.

[Nuclear Radius]

Most nuclei are

nearly spherical.

Namely, many protons and

neutrons collect to compose

a spherical cluster, i.e. a nucleus.

(Precisely speaking, some of them

may not be exactly spherical

but slightly deformed.

We will later discuss

the nuclear deformation.)

According to the experimental

results shown above,

the charge distribution

in a nucleus, ,

is well represented

by a function

This is sometimes called

the Woods-Saxon type

function.

In this function, the parameters , and

are adjusted

to fit the numerical results

to the experimental data.

Adjusting these parameters,

we can well reproduce

the experimental charge distribution.

The value of the parameter R

is the radius of the nucleus.

For example,

the red-colored

R

shows the radius of

the Ca nucleus.

In this way,

precise investigations

of nuclear radii have

carried out for a wide range

of nuclides.

Not only electron scattering

but also various methods

have been used for this purpose

and then it has been clarified that

the nuclear radius

is generally given

by the following formula:

where

is the mass number of the nucleus.

[Nuclear Density and Its Saturation]

From the above formula

for the nuclear radius,

we can easily get

the volume of a nucleus, V, as

Therefore the density of the nucleus is

This means that

the nuclear density is

almost constant

independently of kind of nucleus.

This is called the

saturation of nuclear density.

It is one of the remarkable properties

of atomic nuclei.

From this property, we can see that

the mean value of

the internucleon distance d

is

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