Phenomenological properties of nuclei

1
Phenomenological properties of nuclei
1) Introduction - nucleon structure of
nucleus 2) Sizes of nuclei 3) Masses and
bounding energies of nuclei 4) Energy states of
nuclei 5) Spins
6) Magnetic and electric moments 7) Stability
and instability of nuclei 8) Exotic nuclei 9)
Nature of nuclear forces
2
Introduction nucleon structure of nuclei.
Atomic nucleus consists of nucleons (protons and
neutrons).
Number of protons (atomic number) Z.
Total number nucleons (nucleon number) A.
Number of neutrons N A-Z.
Different nuclei with the same number of protons
isotopes.
Different nuclei nuclides.
Different nuclei with the same number of neutrons
isotones.
Nuclei with N1 Z2 and N2 Z1 mirror nuclei
Different nuclei with the same number of nucleons
isobars.
Neutral atoms have the same number of electrons
inside atomic electron shell as protons inside



nucleus.
Proton number gives also charge of nucleus Qj
Ze
(Direct confirmation of charge value in
scattering experiments from Rutherford equation
for scattering (ds/dO)? f(Z2))
Atomic nucleus can be relatively stable in ground
state or in excited state to higher energy
isomers (t gt 10-9s).
Stable nuclei have A and Z which fulfill
approximately empirical equation
Reliably known nuclei are up to Z112 in present
time (discovery of nuclei with Z114, 116 (Dubna)
needs confirmation).
Nuclei up to Z83 (Bi) have at least one stable
isotope. Po (Z84) has not stable isotope. Th ,
U a Pu have T1/2 comparable with age of Earth.
Maximal number of stable isotopes is for Sn
(Z50) - 10 (A 112, 114, 115, 116, 117, 118,
119, 120, 122, 124).
Total number of known isotopes of one element is
till 38.
Number of known nuclides gt 2800.
3
Sizes of nuclei
Distribution of mass or charge in nucleus are
determined.
We use mainly scattering of charged or neutral
particles on nuclei.
Density ? of matter and charge is constant inside
nucleus and we observe fast density decrease on
the nucleus boundary. The density distribution
can be described very well for spherical nuclei
by relation (Woods-Saxon)
where a is diffusion coefficient. Nucleus radius
R is distance from the center, where density is
half of maximal value. Approximate relation R
f(A) can be derived from measurements
R r0A1/3
where we obtained from measurement r0 1,2(1)
?10-15 m 1,2(2) fm (a 1,8 fm-1). This shows
on permanency of nuclear density. Using Avogardo
constant
we obtain ? ? 1017 kg/m3.
or using proton mass
High energy electron scattering (charge
distribution) ? smaller r0. Neutron scattering
(mass distribution) ? larger r0.
Larger volume of neutron matter is done by larger
number of neutrons at nuclei (in the other case
the volume of protons should be larger because
Coulomb repulsion).
Distribution of mass density connected with
charge ? f(r) measured by electron scattering
with energy 1 GeV
4
Deformed nuclei all nuclei are not spherical,
together with smaller values of deformation of
some nuclei in ground state the superdeformation
(21 ? 31) was observed for highly excited
states. They are determined by measurements of
electric quadruple moments and electromagnetic
transitions between excited states of nuclei.
Neutron and proton halo light nuclei with
relatively large excess of neutrons or protons ?
weakly bounded neutrons and protons form halo
around central part of nucleus.
Experimental determination of nuclei sizes
1) Scattering of different particles on nuclei
Sufficient energy of incident particles is
necessary for studies of sizes r 10-15m. De
Broglie wave length ? h/p lt r
Electrons mec2 ltlt EKIN ? ? hc/EKIN ? EKIN gt
200 MeV
2) Measurement of roentgen spectra of mion atoms
They have mions in place of electrons (mµ
207 me) µ,e interact with nucleus only by
electromagnetic interaction. Mions are 200?
nearer to nucleus ? feel size of nucleus
(K-shell radius is for mion at Pb 3 fm size of
nucleus)
3) Isotopic shift of spectral lines The
splitting of spectral lines is observed
in hyperfine structure of spectra of atoms
with different isotopes depends on charge
distribution nuclear radius.
4) Coulomb energy of nucleus Reduction of
Coulomb energy EC and the same reduction off
binding energy of nucleus (energy of uniformly
charged sphere)
Mirror nuclei same nuclear binding energy,
different Coulomb energy. Difference of binding
energy is given by EC difference.
5) Study of a decay The nuclear radius can be
determined using relation between probability of
a particle production and its kinetic energy.
5
Masses of nuclei
Nucleus has Z protons and NA-Z neutrons. Naive
conception of nuclear masses
M(A,Z) Zmp(A-Z)mn
where mp is proton mass (mp ? 938.27 MeV/c2) and
mn is neutron mass (mn ? 939.56 MeV/c2)
where MeV/c2 1.782?10-30 kg, we use also mass
unit mu u 931.49 MeV/c2 1.660?10-27 kg.
Then mass of nucleus is given by relative atomic
mass ArM(A,Z)/mu.
Real masses are smaller nucleus is stable
against decay because of energy conservation law.
Mass defect ?M
?M(A,Z) M(A,Z) (Zmp (A-Z)mn)
It is equivalent to energy released by connection
of single nucleons to nucleus - binding energy
B(A,Z) - ?M(A,Z) c2
Binding energy per one nucleon B/A
Maximal is for nucleus 56Fe (Z26, B/A8.79 MeV).
Possible energy sources
1) Fusion of light nuclei 2) Fission of heavy
nuclei
8.79 MeV/nucleon ? 1.410-13 J/1,6610-27 kg
8.71013 J/kg
Binding energy per one nucleon for stable nuclei
(gasoline burning 4.7107 J/kg)
6
Measurement of masses and binding energies
Mass spectroscopy
Mass spectrographs and spectrometers use particle
motion in electric and magnetic fields
Mass mp2/2EKIN can be determined by comparison
of momentum and kinetic energy. We use passage
of ions with charge Q through energy filter and
momentum filter, which are realized using
electric and magnetic fields
and then F QE
The study of Audi and Wapstra from 1993
(systematic review of nuclear masses) names 2650
different isotopes. Mass is determined for 1825
of them.
Frequency of revolution in magnetic field of ion
storage ring is used. Momenta are equilibrated by
electron cooling ? for different masses ?
different velocity and frequency.
Comparison of frequencies (masses) of ground and
isomer states of 52Mn. Measured at GSI Darmstadt
Electron cooling of storage ring ESR at GSI
Darmstadt
7
At GSI Darmstadt fragment separator (FSR) makes
possible to produce different isotopes and
storage ring (ESR) makes possible to measure big
number of nuclear masses. Accuracy is ?M 0,1
MeV/c2, that means relative accuracy ?M/M 10-6.
Possibility to measure also very short isotopes t
gt 30 s (with electron cooling), t µs (without
electron cooling).
Similar device is at CERN (ISOLDE)
Exploitation of reaction energy balance
Useful also in the case where mass spectroscopy
is not working (neutral particles).
Determination of neutron mass as example
2) Deuteron mass is md mn mH - B
3) Masses of hydrogen and deuteron are measured
by spectroscopy.
4) Neutron mass is mn (md - mH) B.
Masses of other instable particles and nuclei can
be determined by this method (?M/M 10-8).
Are nucleons localized at nuclei? B/A ? 8 MeV /A
Energy necessary for nucleon separation ? 8 MeV
De Broglie wave length ? h/p ? binding state
condition 2?r n? (n natural number) ? ?/2?
shows typical size. 8 MeV ltlt 939 MeV ?
nonrelativistic approximation
are
Agree with nuclear sizes.
Can be electrons localized at nuclei? Electron
with EKIN 8 MeV is relativistic even
ultrarelativistic
can not
8
Excited energy states
Nucleus can be both in ground state and in state
with higher energy excited state
Every excited state corresponding energy?
energy level
Quantum physics ? discrete values of possible
energies
Scheme of energy levels
Deexcitation of excited nucleus from higher level
to lower one by photon irradiation (gamma ray) or
direct transfer of energy to electron
from electron cloud of atom irradiation of
conversion electron. Nucleus is not changed. Or
by decay (particle emission). Nucleus is changed.
Three types of nuclear excited states 1)
Particle nucleons at excited state EPART 2)
Vibrational vibration of nuclei EVIB 3)
Rotational rotation of deformed nuclei EROT
(quantum spherical object can not have
rotational energy) it is valid EPART gtgt EVIB
gtgt EROT
Energy level structure of 66Cu nucleus (measured
at GANIL France, experiment E243)
9
Obtaining of excited state of nuclei
1) Beta or alpha decays 2) Inelastic scattering
of charged particles or nuclei Coulomb
excitation 3) Nuclear reactions
The big number of different isotopes can be
produced using the fragment separators and
radioactive beams make possible.
Isotope identification obtained by device LISE
(GANIL-France)
Experiment E243 (LISE-GANIL-France)
Measurement of properties of transitions between
excited states
1) Energy spectra and angular distribution of
gamma rays 2) Energy spectra of conversion
electrons
Measurement of excited state properties
Energy spectra and angular distribution of
particles from scattering or reactions
Gamma ray spectrum of deexcitation of 70Ni levels
(experiment E243)
10
Spins of nuclei
Protons and neutrons have spin 1/2. Vector sum of
spins and orbital angular momenta is total
angular momentum of nucleus I which is named as
spin of nucleus
Orbital angular momenta of nucleons have integral
values ? nuclei with even A integral spin


nuclei with odd A half-integral spin
There are valid such rules
3) Components (spin projections) can take values
Iz Ih, (I-1)h, (I-2)h, -(I-1)h, -Ih together
2I1 values.
4) Angular momentum is given by number I
max(Iz). Spin corresponding to orbital angular
momentum of nucleons is only integral I l
0, 1, 2, 3, 4, 5, (s, p, d, f, g, h, ),
intrinsic spin of nucleon is I s 1/2.
11
Magnetic and electric momenta
Magnetic dipole moment µ is connected
to existence of spin I and charge Ze. It is given
by relation
where g is g-factor (sometimes named also as
gyromagnetic ratio) and µj is nuclear magneton
Bohr magneton
For point like particle g 2 (for electron
agreement µe 1.0011596 µB). For nucleons µp
2.79 µj and µn -1.91 µj anomalous magnetic
moments show complicated structure of these
particles.
Magnetic moments of nuclei are only µ -3 µj ?
10 µj, even-even nuclei µ I 0 ? confirmation
of small spins, strong pairing and absence of
electrons at nuclei.
Electric momenta
Electric dipole momentum is connected with
charge polarization of system. Assumption
nuclear charge in the ground state is distributed
uniformly ? electric dipole momentum is zero.
Agree with experiment.
12
Results of measurements
1) Most of nuclei have Q 10-29 ?10-30 m2 ? d
0.1 2) In the region A 150 ? 180 and A 250
large values are measured Q 10-27 m2. They are
larger than nucleus area. ? d 0.2 ? 0.3 ?
deformed nuclei.
Generally apply to
1) All odd electric multiple moments disappeared
2) All even magnetic multiple moments
disappeared 3) For state with total angular
momentum I, mean value of all moments, which
order of multiple L gt 2I disappeared. Nuclei
with I 0,1/2 has not electric quadruple moment.
Measurement of magnetic moments
A) Magnetic moments of nuclei can be obtained
from splitting hyperfine structure (interaction
between electron cloud and nucleus).
13
B) On the base of motion of magnetic dipole
through magnetic fields

• Beam of neutral atoms come through inhomogeneous
  magnetic field ? force F ?Z?BZ/?z
• acts on magnetic moment, oriented it and
  focused beam to the point C.
• (Axe z is in the direction of magnetic field
  changes)
• 2) Homogeneous magnetic field of magnet C not
  created force. In this place orientation of
• magnetic dipole is changed by high frequency
  field (induced by dipole transitions)
• with frequency ? ?Emag /h obtained by
  induction coil.
• 3) Inhomogeneous magnetic field B focused on
  detector only atoms with changed orientation.
• Atoms with not changed orientation are loosed.

C) Measurement of magnetic resonance Sample is
placed to homogeneous magnetic field. Energy
difference corresponding to different
projections of angular momentum IZ ?Emag
gµ?IZB. For dipole transitions ?IZ 1
?Emag h ?L gµB ? ?L (1/h) gµB where ?L
is Larmor frequency. Resonance is observed
by energy absorption at induction coil.
14
Stability and instability of nuclei
Stable nuclei for small A (lt40) is valid Z N,
for heavier nuclei N ? 1,7 Z. This dependence can
be express more accurately by empirical relation
For stable heavy nuclei excess of neutrons ?
charge density and destabilizing influence of
Coulomb repulsion is smaller for larger number
of neutrons.
N Z  number of stable
nuclei even even 156
even odd
48 odd even
50 odd odd 5
Even-even nuclei are more stable ? existence of
pairing
Magic numbers observed values of N and Z with
increased stability.
At 1896 H. Becquerel observed first sign of
instability of nuclei radioactivity. Instable
nuclei irradiate
Alpha decay ? nucleus transformation by 4He
irradiation Beta decay ? nucleus transformation
by e-, e irradiation or capture of electron from
atomic cloud Gamma decay ? nucleus is not
changed, only deexcitation by photon or converse
electron irradiation Spontaneous fission ?
fission of very heavy nuclei to two nuclei Proton
emission ? nucleus transformation by proton
emission
Nuclei with livetime in the ns region are studied
in present time. They are bordered by
proton stability border during leave from
stability curve to proton excess (separative
energy of proton decreases to 0) and neutron
stability border the same for neutrons. Energy
level width G of excited nuclear state and its
decay time t are connected together by relation
tG h. Boundery for decay time G lt ?E (?E
distance of levels) ?E 1 MeV? t gtgt 610-22s.
15
Exotic nuclei
Nuclei far away from stability curve
1) with large excess of neutrons 2) with large
deficit of neutrons (excess of protons)
Effort to study all isotopes between boundaries
of proton and neutron stability.
Double magic nuclei 100Sn is such nucleus
with maximal numbers of neutrons and protons
Firstly observed at GSI Darmstadt at Germany and
at GANIL Caen at France
1) with very high energy 2) with very high
spin 3) with large deformation ? quadruple
moments (superdeformed till hyperdeformed)
Highly excited states
Cases of observation of nucleus 100Sn at GSI
Darmstadt
Device for exotic nuclei studies at GSI Darmstadt
16
Superheavy nuclei for large A and Z stability is
increasing existence of magic numbers ?
existence of stability island. Nuclei up to Z
112 (mainly GSI Darmstadt, JINR Dubna a Berkeley)
were confirmed, Discovery of nuclei with Z 114
(Dubna) a Z 116 a 118 (Berkeley) need
confirmation.
Table of isotopes in the region of superheavy
elements (situation in 2000)
Hypernuclei One or more neutrons are changed by
neutral hyperon ?. ?H3, ?He5, ?Li9, ?O16, ?Fe56,
?Bi209, ??He6, ??Be8). Other hyperons (S, ?, O)
interact strongly with nucleons and they decay
quickly to ? (reactions with strangeness
conversation) ? hypernucleus is not produced.
First discoveries (1952) during cosmic rays
studies. Today more than 33 hypernuclei are
known. Production by intensive meson beams. Decay
time t t? 10-10s.
They make possible to study influence of
strangeness on nuclear force properties
demonstrate existence of attractive forces
between ? and nucleons (B?p lt Bnp).
17
Antinuclei antiproton, antineutron, antilambda,
pozitron and other antiparticles are produced.
Possible existence of antinuclei. Up to now only
the lights antideuteron, antihelium 3
Antiatoms First antiatom (antihydrogen) at CERN
(1996) creation of electron and positron pair
during antiproton movement through
electromagnetic field of nuclei was used (it
resolves problem of positron capture by
antiproton).
One case of antihydrogen anihilation
production of 4 mesons ? (p anti-p) and 2 ?
(e e)
Antiproton decelerator at CERN makes possible
production of thousands antihydrogens, capture
of antiprotons to magnetic trap, mixture with
positrons ? creation of antihydrogen detection
by anihilation
Exotic atoms 1) mion atoms electron is changed
by mion 2) positronium
bound system consists of electron
and positron
3) antiprotonic helium atoms bound system
consists of nucleus
and antiproton
Halo nuclei consist of strongly bounded
core often stable isotope and very weak bounded
neutrons or protons around
Borromean nuclei weakly bound system, every its
part is not bounded alone
18
Nature of nuclear forces
The forces inside nuclei are electromagnetic
interaction (Coulomb repulsion), weak (beta
decay) but mainly strong nuclear interaction (it
bonds nucleus together).
For Coulomb interaction binding energy is B ? Z
(Z-1) ? B/Z ? Z for large Z ? non saturated
forces with long range.
For nuclear force binding energy is B/A ? const
done by short range and saturation of nuclear
forces. Maximal range 1.7 fm
Nuclear forces are attractive (bond nucleus
together), for very short distances (0.4 fm)
they are repulsive (nucleus does not collapse).
More accurate form of nuclear force potential can
be obtained by scattering of nucleons on nucleons
or nuclei.
Charge independency cross sections of nucleon
scattering are not dependent on their electric
charge. ? For nuclear forces neutron and proton
are two different states of single particle -
nucleon. New quantity isospin T is define for
their description. Nucleon has than isospin T
1/2 with two possible orientation TZ 1/2
(proton) and TZ -1/2 (neutron). Formally we
work with isospin as with spin.
19
Spin dependence explains existence of stable
deuteron (it exists only at triplet state s 1
and no at singlet - s 0) and absence of
di-neutron. This property is studied by
scattering experiments using oriented beams and
targets.
Tenzor charakter interaction between two
nucleons depends on angle between spin directions
and direction of join of particles.
Expect strong interaction electric force
influences also. Nucleus has positive charge and
for positive charged particle this force produces
Coulomb barrier (range of electric force is
larger then this of strong force). Appropriate
potential has form V(r) Q/r.
In the case of scattering centrifugal barier
given by angular momentum of incident particle
acts in addition.
20
Exchange nature of nuclear forces
short range ? nonzero rest mass of intermediate
particles. H. Yukawa proposed corresponding
potential
where m is mass of intermediate particle and ?
/mc is its Compton wave length. We put Compton
length equal to range R of nuclear forces and we
determine mass of intermediate particle
Intermediate particles with similar masses were
discovered and named as p mesons. Attractive and
repulsive nuclear force is than intermediated
exchange of charged and neutral mesons
p p - ? n, n p ? p, p p0
? p, n p0 ? n
Protons and neutrons emit and absorb mesons. Why
their masses are not changed?
Uncertainty principle ?E?t ? ? violation of
energy conservation is allowed if it is shorter
then ?/?E. Maximal range of nuclear forces is R
1.7 fm. Then the smallest time of nucleon transit
is ?t R/c. Value of violation of energy
conservation is during emission of meson with
mass mp ?E mpc2. If time of violation will be
?t we obtain for maximal possible energy
violation (meson mass) mpc2 ?c/R (the same as
earlier shown)
Further mesons (?, ?, f ) were found, also
two-meson exchange.