Transcript 投影片 1 - NCHU
Chapter 7 Nuclear Instability
◎
Nuclear decay and energy-level diagrams
●
More on β-decay
◎
The stability of nuclei
●
Spontaneous fission and transition rates
§
7-1 Nuclear decay and energy-level diagrams
Three different types of nuclear decay:
1.
α-decay
2.
β-decay
3.
γ-decay The objective of this chapter is to investigate the kinematics of these decays and in particular to elucidate the role of α- and of β-decay in determining which nuclei are stable and which are not.
γ-ray emitting transitions
1.
In this figure the vertical distance between two levels is the energy difference and the level
X
having the higher energy, is drawn above the one,
Y
, having the lower energy.
2.
A transition from
X
to
Y
normally involves the emission of a photon, the energy difference going into photon energy and energy of the recoil nucleus.
3.
Photon energies involved in this type of transition usually are of about 10 keV up to 3 or 4 MeV and are all referred as
γ-rays
.
4.
γ-rays are emitted when the nucleus makes a transition from an excited state to a state of lower energy.
The best way to study the existence of the heaviest elements, nucleosynthesis in exploding stars, and other phenomena peculiar to the atomic nucleus is to create customized nuclei in an accelerator like Berkeley Lab's 88-Inch Cyclotron, then capture and analyze the gamma rays these nuclei emit when they disintegrate. The Lab's Nuclear Science Division (NSD) has been a leader in building high resolution gamma-ray detectors and was the original home of the Gammasphere, the world's most sensitive. Now NSD is leading a multi-institutional collaboration to build Gammasphere's successor, the proposed Gamma-Ray Energy Tracking Array, or GRETA. http://www.lbl.gov/Science-Articles/Archive/sabl/2007/Feb/GRETINA.html
Quantum states in 257 No and 253 Fm
Energy spectrum observed through γ-ray emitting transitions
γ-ray spectrum of 257 No
α-particle decay
(
Z
,
A
) (
Z
2 ,
A
4 ) 2 4 He
Q
[
M
(
Z
,
A
)
M
(
Z
2 ,
A
4 )
M
( 2 , 4 )]
c
2
The energy-level diagram for two nucleic connected by α-decay The energy-level diagram for the α-decay of 242 Pu
The available energy
Q
α goes into the kinetic energies of the α-particle and of the recoil of the daughter nucleus.
If
Q
α > 0, α-decay is energetically possible; however, it may not occur for other reasons.
The expected alpha-decay chain of new isotope 233 Am and alpha-particle energy spectrum. In the spectrum the decay chain is observed with the
6.78 MeV
alpha-particle originating from 233 Am decay.
Intensity against alpha energy for four isotopes, note that the line width is wide and some of the fine details can not be seen. This is for liquid scintillation counting where random effects cause a variation in the number of visible photons generated per alpha decay
§
7-2 More on β-decay
The apparent process in β-decay is he conversion of nucleus (
Z
,
A
) into nucleus (
Z
+1,
A
) and an
electron (e )
: (
Z
,
A
) (
Z
1 ,
A
) e It is actually the conversion of a bound neutron (n) into a bound proton (p).
n p e
β - decay
For some proton-rich nuclei they can frequently undergo β-decay in which a
positron (e + )
is emitted.
p n e
β + - decay
A proton-rich nucleus can capture an atomic electron and thereby change a proton into a neutron.
e (
Z
,
A
) (
Z
1 ,
A
) or e p n
electron capture
The electron is captured usually from the K-shell but can be from the L, M, N, or even higher shell. In this process the electron in annihilated.
This experimental energy spectrum is from G. J. Neary, Proc. Phys. Soc. (London), A175, 71 (1940).
(38%) (19%) (43%)
To the right is a fit to the vetoed spectrum. The peaks from 99 Tc and 100 Ru don't help resolve the miniscule 100 Mo peak. The spectrum would look much better if we could remove all the 99 Tc contamination and veto more βs, which would also help by getting rid of the 100 Ru x rays that come with the βs.
Magnetic Trapping of Ultra-cold Neutrons
Measurement of the
beta
-
decay
For more information, please see our publication P. R. Huffman et al., Nature, 403 , 62 (2000).
Electrons emitted through a process called the
internal conversion
Internal conversion
is a process by which a nuclear excited state decays by the direct ejection of one of its atomic electrons; it occurs normally in competition with photon emission.
Early mysteries concerning the β- decay:
1. The kinetic energy spectrum of the emitted electrons is continuous.
2. Consider the following decay. It seems to violate the law of angular momentum conservation.
14 6 C 14 7 N e -
0 1 1/2 ?
There is no way that angular momentum can be conserved in the decay.
In 1930 Pauli made a hypothesis that provided a solution to these difficulties and that has satisfied all experimental tests.
He proposed that an electrically
neutral particle of spin 1/2
is created and emitted at the same time as the electron (or positron) in β-decay.
Wolfgang Ernst Pauli Austrian–Swiss physicist (1900–1958)
The particle is called a
neutrino
(symbol,
ν
) and it can take a share of the energy because in β-decay there is now a
three body configuration
of the final state.
It turns out that nature has three kinds of neutrinos each with its own antiparticle and mass.
( e , e ) ( μ , μ ) ( τ , τ )
Three flavors of neutrinos
We need to label the neutrinos in nuclear β-decay in the following fashion: β - decay (
Z
,
A
) (
Z
1 ,
A
) e e β + - decay Electron capture (
Z
,
A
) (
Z
1 ,
A
) e e e (
Z
,
A
) (
Z
1 ,
A
) e In order to consider the energetics of β-decay, we need to know the mass of the neutrino emitted in β-decay. It is known to be less than 18 eV and since this is small compared to the total energy released in most β-decays we shall assume that the mass is zero. In fact the neutrino mass would be of considerable significance in cosmology and in theories of elementary particles.
Neutrino’s mass is not zero.
universe-review.ca/R15-13-neutrino.htm
Free nucleon decays:
(1).
A free neutron undergoes β-decay with a mean life time τ = 898 seconds .
n p e ν e Q β = [
M n
–
(
M p
+
m e
)]
c
2 = [939.573 – (938.791 + 0.511)] MeV =
0.782 MeV > 0
This process is certainly energetically possible since Q β which is larger than zero.
=
0.782 MeV (2).
Consider the case for a free proton: p n e ν e Q β = [
M p
–
(
M n
+
m e
)]
c
2 = [938.791 – (939.573 + 0.511)] MeV =
–
1.293 MeV < 0
This process is energetically impossible since Q β which is smaller than zero.
=
–
1.293 MeV
This is a fortunate situation as the stability of protons (on the time scale of >>
10 14 years
) is essential to the existence of the universe and of ourselves.
A diver takes a swim in the IMB detector
.
The IMB Proton Decay Detector in the Fermi Lab
The IMB detector was a
60-foot (18.3 m)cube
of ultra-pure water constructed in a salt mine underneath Lake Erie. The water was surrounded by
2000
light-sensitive phototubes, designed to detect proton decay. The experiment became famous for the observation of the neutrino burst emitted by a nearby Supernova (exploding star).
http://www.foster08.com/about/?id=science
Super-K is located
1,000 m
underground in the Mozumi Mine ( Kamioka Mining and Smelting Co.
) in Hida city (formerly Kamioka town), Gifu , Japan . It consists of
50,000 tons (1 ton = 10 3 kg)
of pure water surrounded by about
11,200
photomultiplier tubes. The cylindrical structure is
41.4 m
tall and
39.3 m
across. http://www.arch102-07.form-ula.com/?p=1537
(3).
Electron capture in a hydrogen atom e p n ν e Q β = [(
M p
+
m
e ) –
M n
]
c
2 = [(938.791+0.511) – 939.573] MeV =
–
0.271 MeV < 0
This process is unlikely to happen as its Q β value is seen smaller than zero. Furthermore the safety of the proton against electron capture follows immediately from the existence of free neutron decay.
Energy conditions in β-decay and electron capture in terms of nuclear masses, M(Z, A):
: (
Z, A
) (
Z
1
,A
) e ν e Q β = [
M
(
Z
,
A
) –
M
(
Z
+ 1,
A
) –
m e
]
c
2 > 0 : (
Z, A
) (
Z
1
,A
) e ν e EC : (
Z, A
) e (
Z
1
,A
) ν e Q β = [
M
(
Z
,
A
) –
M
(
Z
–
1,
A
) –
m e
]
c
2 Q EC = [
M
(
Z
,
A
) –
M
(
Z
–
1,
A
)
+
m e
]
c
2 > 0 > 0 If a condition is satisfied, then the appropriate decay is possible and the excess energy available is shared as kinetic energy among the products in a manner which conserves linear momentum.
Note that electron capture can sometimes occur when β + -decay is impossible.
§
7- 3 The stability of nuclei
In this figure the stable nuclei lie on or near a curve of
N
against
Z
.
For those nuclei which are not in this region of stability β-decay can occur.
Beta decay process while keeping
A
constant can step
Z
to bring the nucleus onto a stable position in the chart.
For an unstable
proton-rich
nucleus a positron is emitted so as to step down its atomic number
Z
by 1 while keeping its mass number
A
constant and moving toward the stable region.
a For an unstable
neutron-rich
nucleus an electron is emitted so as to step up its atomic number
Z
by 1 while keeping its mass number
A
a constant and moving toward the stable region.
Stable isobar of
A = 101
We are therefore interested in the nuclear mass of isobars (
fixed A
) as a function of
Z
.
In this figure the nuclear mass of
A = 101
is shown: The masses are calculated using the semi empirical mass formula and a smooth curve of no physical significance is drawn through the points. The actual atomic masses are given by
open points
.
Since
N > Z
for most nuclei, an increase in
Z
decreases the asymmetry contribution to the mass. However, the increase in
Z
increases the Coulomb energy contribution. On the left of the minimum in the mass the decrease wins over the increase and the atomic mass decreases with
Z
. On the right the increase in Coulomb energy wins and the mass increases.
1.
On the left limb as
Z
changes from
41→42→43→44
every step so that β decay can occur at each step.
the atomic mass decreases at
2.
The mass changes on the right are also greater than can occur at each step. Actually
45→44 2m
e c
2
, so β + decay or electron capture can go by electron capture only but not the β + decay.
β-decay in
odd A
and
even A
isobars ― from chapter 4
For odd-
A
isobars, δ = 0, and equation (14) gives
a single parabola
, which is shown in the figure (
a
) for a typical case. We will see later that if
M
(
A
,
Z
) c 2
A
Z
Z
2 (4. 14)
M
(
A
,
Z
) >
M
(
A
,
Z
+1) beta (electron) decay takes place from
Z
to
Z
+1 (4. 15)
M
(
A
,
Z
) >
M
(
A
,
Z
-1 ) electron capture and perhaps positron decay takes place from
Z
to
Z
- 1 It is clear from the figure (a) that for odd-
A
nuclides there can be only one stable isobar.
M
(
A
,
Z
) c 2
A
Z
Z
2 (4. 14) For even-
A
isobars, two parabolas are generated by the equation (14), differing in mass by 2δ . A typical case is given in the figure (
b
).
Depending on the curvature of the parabolas and the separation 2δ , there can be several stable even-even isobars. Figure (
b
) shows that for certain odd-odd nuclides both conditions (15) are met so that
electron and positron decay
from the identical nuclide are possible and do indeed occur.
Another example
In the case of
even-A
nuclei
even-Z
nuclei have a binding energy advantage arising from the pairing term, whereas the
odd-Z
nuclei have a lower binding energy due to the opposite contribution from this term. Thus there are two curves of isobar atomic mass against
Z
and alternate
Z
lie on different curves.
In this figure nucleus
Z = 43
can decay by electron capture to
Z = 42
or by β –
-
decay to
Z = 44
. The prediction is that there are two stable isobars for
A = 100
, namely
Z = 42
and
44
, which is true.
40 K 19 40 A 18 40 20 Ca
This situation in even-A nuclei sometimes leaves an odd-odd isobar energetically able to decay by all modes. There is indeed an example of
40
K
19
which is able to decay in three different modes with different branching ratios.
An examination of the even-A nuclei suggests two conclusions:
1.
there is no stable odd-odd nucleus;
2
. many even-even nuclei can have more than one stable isobar.
Conclusion 1
is almost true; there are
four real exceptions
among the light nuclei, namely
2 H 1
,
6 Li 3
,
10 B 5
, and
14 N 7
. In the case of
2 H 1
, it is the only bound system with
A = 2
. At the other
A
, the masses are changing rapidly with
Z
and the two parabolas of
A = 100
as shown in the figure become, at this low
Z
, narrower, and have steeper sides. The result is that each of these values of
A
, the nuclei one place away in
Z
from each of these odd-odd nuclei are heavier and there can be no decay to these neighbors.
Conclusion 2
is true without any exception.
Away from the line of stability
β-decay
is a certainty. This conclusion becomes evident when we consider regions fairly close to the line of stability.
Nuclei that are very
rich in protons, or in neutrons,
may be beyond the appropriate
drip line
, where it is energetically possible to emit a proton (or neutron) as a direct relief of the richness. Such a process occurs relatively very rapidly and so these nuclei have very short mean lives, in fact so short in some cases that the nucleus may not have a distinct existence before the neutron is emitted and the producing process and decay become a
nuclear reaction
.
Experimentally determined neutron drip line Nature 499(2007)992 The best prediction of the neutron drip line for heavier elements Neutron drip line: The line on the Z, N plane where the neutron separation energy is zero.
We now have to apply the energy conditions for α-decay to occur in real nuclei and to find where in the periodic table it is expected to occur.
(
Z
,
A
) (
Z
2 ,
A
4 ) 4 2 He Rewrite the definition of
Q
α
in terms of the nuclear binding energies.
Q
B
(
Z
2 ,
A
4 )
B
( 2 , 4 )
B
(
Z
,
A
) (1) d d
B A
d d
A
d
A
d
A
d
A
d
A A B A B A B A
B A
B A
d
A
d
A
Thus α-decay is energetically allowed if
B
( 2 , 4 )
B
(
Z
,
A
)
B
(
Z
2 ,
A
4 ) 4 d
B
d
A
4
A
d (
B
/ d
A A
)
B A
(2)
B
( 2 , 4 )
B
(
Z
,
A
)
B
(
Z
2 ,
A
4 ) d
B
4 d
A
4
A
d (
B
/ d
A A
)
B A
A = 151
Above
A ≈ 120
,
d(B/A)/dA
about
−7.7
×
10 −3 MeV
. Now is
B(2,4) ,
the helium nuclear binding energy, is
28.3 MeV
, so the critical
A
must satisfy the following relation: 28 .
3 4
B A
7 .
7 10 3
A
which is
B A
7 .
075 7 .
7 10 3
A
(3) Above this
A
the inequality of equation (3) is satisfied by most nuclei and α-decay becomes, in principle, energetically possible. In fact from
A = 144
to
A = 206
, 7 α emitters are known amongst the naturally occurring nuclides.
From A = 144 to A =206
From
A = 144
to
A =206
, there are
7
α-emitters of naturally occurring nuclides. When α-emitters are found in this range of
A
, the energies of the emitted α-particle are normally less than
3 MeV
. It is known that the lower the energy release the greater is the lifetime. Their existence implies mean lifetimes comparable to or greater than
the age of the earth
(about
4
×
10 9
years). Most nuclei in this range on the line stability may be energetically able to decay by α-emission. They do not do so at a detectable level because the transition rate is too small.
Above Z = 82 (A > 206)
Above
Z = 82
many naturally occurring α-emitters are found, many with
short lives
.
Why are they to be found when their lifetime is so short?
Most of the heavy nuclei to be found on earth were probably produced in one or more
supernova explosions
of early massive stars. Such explosions can produce very heavy nuclei including
trans-uranic elements (Z > 92)
and their subsequent decay by α-emission will take them down the periodic table in steps of
ΔA = −4
. Each α-decay increases the ration
N/Z
until a β decay intervenes to restore the nucleus closer to the line of stability.
Very long lifetime comparable to the age of the earth Relatively long lifetime Fast-decaying daughter nuclei are in secular equilibrium.
Large binding energy per nucleon
(7.08 MeV)
of the
α particle
makes
α-decay
possible for heavy unstable nuclei. It is interesting to note that the nucleon in
12 C 6
are even more strongly bound
(7.6 MeV)
than are those in
4 He 2
. As a result decay by
12 C 6
nucleus emission is energetically possible in some heavy nuclei. Decay by
14 C 6
emission has been found but it is very rare.
223 Ra 209 Pb 14 C The probability for this process is very small, about 10-9 relative to the α-decay.
However, all these processes are a part of a spectrum of possibilities in which a heavy nucleus breaks into two (or more) parts. These are called
“spontaneous fission”.
238 92 U 145 57 La 90 35 Br 3 n