Nuclear
and Particle Physics
Brian
R Martin
First
edition, February 2006
printing
Corrections
and Clarifications
(There is a separate section below for corrections to solutions
to the problems)
(The
notation is: line n means n lines from top, including equations; line
–n means n lines from the bottom, excluding footnotes. )
p6, line 8-9: The statement
about the magnitude of the magnetic moment is wrong. It should be
replaced by ' ....where
S is its spin
vector. Magnetic moment is a vector, and the value
mu (Greek) tabulated is the
z-component when the
z-component of
spin has is maximum
value, i.e
mu
(Greek)
= qh(hbar)/2m.'
p4, lines 9, 11,
15, 20 and p46, line -10: 'Fermi' should of
course be 'Pauli'. How 'Pauli'
became 'Fermi' in the text and survived double proof-reading is a
mystery, particularly as it is correct in the previous book "Particle
Physics" by Martin & Shaw and correct elsewhere in the present book!
p5, footnote 13: delete last sentence
after word 'aces'. There are of course only three families of
quarks!
p22, Eqn (1.42): Strictly, the
algebraic part of this equation is true for the vector part of the weak
interaction. Thus to retain the numerical value, the middle part of the
equation should be deleted, as well as the words 'from Equation (1.36)'
on the line above.
p42, Eqn (2.25): On the rhs
the integral is over the vector
r
and for consistency the integral should be divided by Ze, the
normalization factor.
p50, lines 2–4:
NC(t) is
not the population of the final
stable state, so the following change is needed.
replace:
….. time, and
NC(t) for
the final stable species rises monotonically,
NB(t) for an intermediate species
rises to a maximum before falling. Note that at any time the sum of the
components is a constant, as expected.
with:
…. time, the relative populations
NB(t) and
NC(t) of the intermediate species rise
to maxima before falling. The population of the final stable species
(not shown) will rise monotonically.
The current Figure 2.8 does not illustrate the points above very well.
The figure below, specifically for the decay sequence (2.45) is much
better.
p51-52: The argument leading to the
pairing term might suggest that
this can be deduced from the Fig 2.9 (i.e. the Fermi gas model) which
is not correct. It should be replaced with:
The final contribution is the empirical pairing term with the form
(2.52). This arises from the tendency of like nucleons in the same
spatial state to couple pairwise to configurations with spin-0. When
coupled like this, the wavefunctions of the two nucleons heavily
overlap and so on average they are closer together than when coupled in
other configurations, and hence are more tightly bound. When we have an
odd number of nucleons, this term does not contribute. Thus, when both
Z and
N are odd, we gain binding energy
by converting one of the odd protons to a neutron (or vice versa) so
that it can now form a pair with its formerly odd partner. The evidence
for this is that there are only four stable nuclei with odd N and Z,
whereas there are 167 with even
N
and
Z. The form used for
f5 is empirical, but
f(A)=a5/sqrt(A) represents the
trend of the data for the pairing energies and is often used.
p73, line 20: change
evidence that
to evidence
from decays that
p74, line -12:
change accuracy.
to accuracy in reactions.
p74, line -13:
change conserved,
to conserved in decays,
These changes are to clarify that the evidence for lepton number
violation comes from decays and it is still OK to assume conservation
in neutrino reactions.
p82: The comments on the SNO
experiment are confused (and wrong in places). The last part of the
paragraph starting from the sentence 'More recent experiments .....'
should be replaced with the paragraph below.
A more recent experiment (SNO) has studied the reactions:
(a) νe + d → e– + p + p ,
(b) νx + d → νx +p +
n , (c) νx + e– → νx + e– , (3.33)
where x denotes any lepton flavour (e, μ, τ) and d is the deuteron. The
cross-section for (b) is independent of the lepton flavour (this is a
consequence of ‘lepton universality discussed in the next section) and
hence independent of any possible oscillations. Since the observed flux
is consistent with expectations, this confirms the correctness of the
solar model. On the other hand, the observed flux from (a) is only
about 1/3 of expectations, implying that about 2/3 of the electron
neutrinos from the original decay process (3.32) have transformed to μ
and/or τ neutrinos before being detected at the surface of Earth. The
flux for (c) would then be due to a mixture of approximately 1/3
electron neutrinos and 2/3 μ/τ neutrinos and the observed flux,
which is also below expectations for no oscillations, is consistent
with this assumption.
p106, Table 3.6: the
expressions for the
K and
K* masses are wrong. The correct
expression follow directly from Eqn (3.81) a line or two above and are:
K = m + ms –(3a / 4 m ms ) and K* = m + ms +(a / 4 m
ms)
Eqn (3.82) should be changed in the same way.
p169, Eqn (5.26): lhs should
be –
Q**2
p170, line 10: Q becomes
q ;
Eqn (5.30): all the
Q's
become q's :
Eqn (5.31): the
Q**2 and
Q in the
middle of this equation become
lower case
q's
p290,
line 8 and footnote 17: The discovery of magnetic resonance is
not correctly attributed. Bloch and Purcell shared the 1952 Nobel Prize
in Physics for the
'development of
new methods for nuclear magnetic precision measurements'. The original
discovery is due to Isidor Rabi who received the 1944 Nobel Prize in
Physics for his 'resonance method for recording the magnetic properties
of atomic nuclei'.
Corrections
to problems and their solutions
(For
completeness I have listed even trivial typographical errors. The
notation is: line n means n lines from top, including equations; line
–n means n lines from the bottom, excluding footnotes. Comments are in
[ ] brackets.)
p30,
Problem 1.1:
Equation (1.35)
becomes
the Yukawa potential (1.35)
p110, Problem 3.11:
rewording: .....
Assuming a two-component model with maximal mixing (alpha = 45 degrees)
..... mass difference of the anti-electron neutrino and its
oscillating partner.
p150, Problem 4.13: The
density of iron should be 1.14 x 10^4 kg m^-3. The solution is
therefore changed. See below p370
p214, problem 6.6: Insert: Use sin(thetaW)^2 = 1/4.
p252, Problem 7.5: Delete the
factor
e from the expression
for the quadrupole moment
p354, Problem C.2: denominator
in expression for
d
should be cot and not cosec (solution is correct)
p357, Solution to Problem 1.8: the
solution for
R is
dimensionless, not fm
p358, Solution to Problem 2.1: upper
limits in integrals is
a not
r
p359, Solution to Problem 2.3: The
numerical value should be 4.88 fm and not 6.56 fm as given.
p360, Solution to Problem 2.11: solution
269.15
becomes 269.13
p361, Solution to problem 2.13:
the log term should be 0.5 x 10^7, so the final value is 2.4,
not 2.6. Also, since Pb(204) is stable, the term in tau(204) should be
ignored.
p365, Solution to Problem 3.8: there
should be a factor hbar**2 dividing the spin terms. The final solution
is correct.
p365, Solution to Problem 3.11: There
is a numerical error. Using 0 < P(e to x) < 0.3 gives 0 < m^2
< 6.9x10^(-3)
p366,
Solution to Problem 4.1: second minus in first equation
should be a plus. The final solution is correct.
p370, Solution to Problem 4.10: the
term
mc^2 in the expression
for
n should be just
m.
p370, Solution Problem 4.13: last
line, because of the correction on p150 (see above), 10^33
becomes 10^30
and hence
l = 2.3 x 10^3 m
p370, Solution to Problem 4.14: The
target contains 5.30 x 10^24 protons and not 1.07 x 10^25, and there
are two photons per interaction. Thus the number of photons produced
per second is 848.
p380, Solution to Problem 6.9: replace
almost 20 times with
about 10 times.
p380, Solution to Problem 6.8: no propagator 'means'
no propagator with a W-mass factor
p382, Solution to Problem 7.3: in
line-4
neutron becomes
proton
In the second suggested method of explaining the spin-parity of the
excited state, it would more likely that the two d5/2 protons would
combine to give Jp = 0+, which would not give the desired result. So,
an alternative would be to promote one of the p3/2 neutrons to
the d5/2 shell, so that the final neutron and proton in d5/2
could combine to give JP = 2+, which when combined with the unpaired
3/2- neutron would give the required quantum numbers.
p384, Solution to Problem 7.7: the
factor R has been omitted in the numerical solution. Thus line 1
becomes
t1/2(Th) = t1/2(Cf) R(Th) [exp(G(Th) – exp(G(Cf))] / R(Cf)
Then t1/2(Th) changes from 4.0 yrs to 3.9 yrs.
p384, Solution to Problem 7.10: The
form of the indefinite integral has been incorrectly printed in the
solution. (It is given correctly in the solution to Problem 7.11.)
However, the value for
F is 3
x 10^(-10) as given.
p391, Solution to Problem B.8: line
before the end,
p and
E should have primes. The final
solution is correct.
p391, Soln to Problem B.9: This
has used the proton mass 0.983 GeV/c**2. Using the correct value 0.938
GeV/c**2 changes the final value from 0.54 m to 0.58 m.
p392, Solution to Problem B.10: on
the last line the prime should be on the first
E and not the second. The final
solution is correct.
Minor
typographical errors
(For completeness I have
listed even trivial typographical errors. The notation is: line n means
n lines from top, including equations; line –n means n lines from the
bottom, excluding footnotes. Comments are in [ ] brackets.)
pxi,
line 11: subject which
becomes
subject, which [insert comma]
pxv, table of constants:
exponent for (hbar*c) squared should be -32 (not -31)
p6, line 10: this relation,
becomes this relation 17, [insert
footnote number 17]
p9, footnote 23: 1958
becomes
1959
p11, line 9:
the subscript
l on
R(nl) is in the wrong font
[should be Times italic]
p18, lines 5:
four-vector
becomes
four-momentum
p19, Eqn (1.33): c**4
becomes c**2
p22, line 7: there should be a
minus sign before the (four-momentum)
q-squared
p22, line 10: GsubF
becomes 2sqrt(2) GsubF
p28, caption
Fig.1.8: Breit--Wigner
becomes
Breit-Wigner [single dash]
p30, line 10:
XV
becomes xv [lower case]
p38, line -5;
(2.16)
becomes (2.14)
p38, footnote 4: Chapter 6
becomes Chapter 5
p38, Eqn (2.17):
q in the exponent of the
exponential should be
q (ie
bold)
p39, footnote 6: Chapter 6
becomes Chapter 5
p42, Eqn (2.31) This is for
the
nuclear not the charge
radius
p56, caption
Fig.2.12: SEMF--possible
becomes
SEMF-possible [single dash]
p56, axis label Fig.2.12: Atomic
number
A becomes Atomic
number
Z
p58, caption Fig.2.13:
odd--odd
becomes odd-odd
[single dash]
p58, axis label Fig.2.13: Atomic number
A becomes Atomic number
Z
p77, line 18: the E in the term
Esub2 should be italic
p80,
caption Fig.3.3:
illustration--with
becomes illustration-with
[single dash]
p86, line -7: Chapter 6
becomes Chapter 5
p93,
line
-11:
I = 1/2
becomes I =
1/2 [bold
1/2]
p93, line
-8; I
= 1
becomes I =
1 [bold
1]
p93, line -4: I
= 3/2
becomes I =
3/2 [bold
3/2]
p95, line 12:
I
= 3/2
becomes I =
3/2 [bold
3/2]
p98, Eqn (3.61): the final
minus sign should be a plus sign
p99, Figure 3.11(a): one of
the -1/2 should 1/2
p104, Table 3.5, line 4 of caption:
--
becomes - [single dash]
p107, Eqn (3.88): The
expression on the lhs should be the square of the sum of the spins, not
the sum of the squared spins
p107, Eqn (3.90) For
consistency, the term
b
should be divided by hbar**2
p108, Eqn (3.91) For
consistency, the first term
b
should be divided by hbar**2
p108, Table 3.7: in the
expression for sigma*, the tem 1/m should be 1/(m**2)
p108, Table 3.7: in the
expression for omega, the tem 3b/(ms**2) should be 3b/(4ms**2)
p119,
caption Fig.4.5:
frequency--thus
becomes frequency-thus
[single dash]
p128, Eqn (4.18): the minus
sign in front of the rhs should be deleted
p154,
caption Fig.5.1:
quark--quark
becomes
quark-quark
[single dash]
p155,
caption Fig.5.2:
gluon--gluon
becomes gluon-gluon
[single dash]
p156, line 1: three
becomes four
p156, line -10: many
becomes several
p159, caption Fig. 5.5: the
labels 2--
become 2++, as
correctly given in Table 5.2
p160,
Eqn.
(5.7):
V(r)
= -a/r becomes V(r) = -a(hc)/r [extra factor hc in numerator on rhs -
note that h is really hbar]
p160,
Eqn. (5.8):
V(r)
= br
becomes V(r) = -br/(hc)
[extra factor hc in demoninator on rhs - note
that h is really hbar]
p160, Eqn. (5.9): this should
ammended to take account of the two changes above
p161, line 12: c^4
becomes c^2
p164,
caption Fig.5.9:
quark--quark
becomes quark-quark
[single dash]
p165,
caption Fig.5.10:
electron--positron
becomes electron-positron
[single dash]
p166,
caption Fig.5.11:
electron--positron
becomes electron-positron
[single dash]
p169, caption Fig.5.13:
e
becomes e [italic]
p169,
caption Fig.5.13:
or becomes or [not italic]
p174, line -4: there should be
a factor of 18/5 multiplying the charged lepton structure function
F2 (as in Eqn (5.42) just above.
p185,
Fig.6.3:
P
is in the wrong font
p194, Eqn (6.24): rhs should
be 4.2 x 10(-3) approx equal to 0.6 alpha
p196,
caption Fig.6.12:
quark--lepton
becomes quark-lepton
[single dash]
p199,
Eqn (6.35): GsubF
becomes
2sqrt(2) GsubF
p199, Eqn (6.36): lhs should
be divided by sqrt(2)
p202, Fig 6.16: the
W-minus label on the exchanged
particle should be
W-plus
p204, line -7:
processe
becomes
process
p219, footnote 6: Chapter
6
becomes Chapter 5
p226,
footnote line 1:
nuclei.
becomes nuclei,
[full stop becomes comma]
p226, line 1: dipole
becomes quadrupole
p226,
Eqn
(7.24):
the
rhs of this equation should contain an extra factor of hbar squared
p227, Figure 7.4: the 1F state
is split into 1F5/2 and a 1F7/2 states. The former is incorrectly
written as 1F1/2
p227,
caption Fig.7.4:
spin--orbit
becomes spin-orbit
[single dash]
p233, Eqns (7.34) and (7.35): delete
the factor
e from the rhs of
these equations
p235, Eqn (7.40): in the
denominator, (2j+1)
becomes (2j+3)
p236, line 6: Neils
becomes Niels
p243, line 6: insert a full
stop after the word 'space'
p243, Eqn (7.60): lhs should
be divided by sqrt(2)
p259,
Eqn
(8.7):
the
numerator of the lhs of this equation should contain an extra
factor -
N(t) i.e.
(N(t+deltat) - N(t))/deltat
p261,
caption
Fig.8.2: reactor--the
becomes reactor-the
[single dash]
p264,
line
6:
is
greatly
becomes is also
greatly
p268, Eqn (8.27): the letter O
in the oxygen nucleus is not italic
p273, Eqn (8.45a): H on rhs
becomes He
p274,
caption Fig.8.2:
d--d
becomes d-d [single dash]
p274,
caption Fig.8.2:
d--t
becomes d-t [single dash]
p277,
caption Fig.8.8:
EFDA--JET
becomes EFDA-JET [single
dash]
p301,
caption Fig.9.3:
energy--momentum
becomes energy-momentum
[single dash]
p307, line -9: Universe
becomes universe [lowers case u]
p309,
caption Fig.9.7:
(IBM)--in
becomes (IBM)-in
[single dash]
p320,
caption Fig.9.11:
gluon--gluon
becomes gluon-gluon
[single dash]
p321,
caption Fig.9.12:
gold--gold
becomes gold-gold
[single dash]
p333, Eqn (A.13): the
denominator 2 in each term should be
L
p333,
Eqn (A.14): following from the above, the denominator in
the last tem
becomes 2
mL^2
p334,
line 7: (L / pi) becomes (pi / L).
The rest of the derivation is correct.
p336, line 9: (A.22)
becomes (A.26)
p393, line 6: Fernlow
becomes Fernow
p394, header: this should be
‘References’, not ‘Bibliography’.
p396,
Bibliography,
line 3: section
which follows
becomes
section.
p404,
Index, rh
column: insert
blank line after
entry 'Fusion reactors, tokamak'
p404,
Index, rh column: remove
blank line after
entry 'gamma-rays 4, use in medical imaging 283-284'
p405, Index, lh column: insert
extra entry
'Gottfried sum rule 179' before entry 'Golden Rule 333-338'
p406, rh
column:
in
entry 'Neutrinos 4, Limits on ...' , the L should be lower case
Comments
1.
The
2004
edition of the Particle Data Group's 'Review of Particle Physics' has
been superceded by the 2006 edition: W.-M. Yao et al. (2006) Journal of Physics G33, 1-1232
and some of the
numerical data quoted in the book has been changed slightly.
2. A number of other references to
Nobel Prize winners could have been included in footnotes as follows:
p6: Polykarp Kusch shared the
1955 Nobel Prize in Physics for his precision determination of the
magnetic moment of the electron.
p62: Hans Bethe received the
1967 Nobel Prize in Physics for his contributions to the theory of
nuclear reactions, especially his discoveries concerning the energy
production in stars (discussed briefly in Sec. 8.2.2).
p269: William Fowler shared the 1983
Nobel Prize in Physics for
his studies of nuclear reactions of importance in the
formation of chemical elements in stars.
p290: see Correction 4 above.
Last
updated February 2007
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