Basdevant J.-L., Rich J., Spiro M. Fundamentals in Nuclear Physics: From Nuclear Structure to Cosmology

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8.4 Nuclear astronomy 383

− 1

H →

H ν

Q=1.442 MeV . (8.79)

This reaction sometimes substitutes for (8.73). Finally, the highest energy

neutrinos come from the very rare “hep” reaction

He →

He e

Q=18.8MeV ,. (8.80)

As explained in Sect. 8.2.1, the Sun is dominated by the PPI cycle so the

solar neutrino spectrum is dominated by ν

. Figure 8.13 shows the calculated

ﬂux [73]. The ﬂuxes of the three important neutrinos types are in the ratio

: ν

=1:0.08 : 10

−4

hep

pep

0.1 1.0

E (MeV)

−2

Fig. 8.13. The solar-neutrino ﬂux at Earth predicted by standard solar models [73].

For the continuous components, the ﬂux is in units of m

−2

−1

MeV

−1

. The ﬂux of

the line components is given in m

−2

−1

All solar neutrinos are produced as ν

. As explained in Sect. 4.4, this

corresponds to a mixture of three massive neutrinos, ν

, ν

and ν

. Depend-

ing on the neutrino masses and mixing angles, these neutrinos should reach

us after being aﬀected by vacuum oscillations and/or the MSW eﬀect. The

original ν

spectrum of Fig. 8.13 is transformed into an energy-dependent

combination of ν

, ν

. Solar-neutrino detectors based on neutral-current

reactions have rates that are independent of the mixture but charged-current

detectors are only sensitive to the ν

-component.

The diﬃculty of detecting solar neutrinos comes from their tiny interac-

tion cross-sections. For solar neutrinos of energy ∼ 1MeV, a ﬁrst estimate of

384 8. Nuclear Astrophysics

the cross sections is then σ ∼ G

1MeV

/(¯hc)

which is about 5 × 10

−48

Taking the full neutrino ﬂux, this gives an event rate of at most a few events

per day for a 1 ton detector. This sets the scale for experiments.

It should be emphasized that the rate is much less than the decay rate

from natural radioactivity even in the most pure material, say, 10

−9

uranium.

Water Cherenkov detectors. Because of these diﬃculties, only the high-

energy ν

can be said to have been satisfactorily investigated. These neu-

trinos have energies that are suﬃciently high that the ﬁnal-state particles

have energies greater than the energies of decay products of natural radioac-

tivity. This fact has allowed them to be detected by two large underground

water Cherenkov detectors, Superkamiokande [82] and the Sudbury Neutrino

Observatory (SNO) [81].

The most complete results have been obtained by SNO, operating in a

nickel mine in Sudbury, Ontario, and using 1000 ton of heavy water as a

neutrino detector.

A schematic of the apparatus is shown in Fig. 8.14. The

heavy water is surrounded by photomultipliers that can measure Cherenkov

light emitted by relativistic particles.

This makes the detector sensitive to

electrons of energy > 1 MeV and to photons of energy > 2 MeV that produce

electrons through Compton scattering.

The reactions that SNO uses to detect neutrinos are

H → e

−

pp E

> 1.44 MeV , (8.81)

H → νpn E

> 2.2MeV . (8.82)

ν e

−

→ νe

−

, (8.83)

The charged current reaction dissociation of

H (8.81) is sensitive only to ν

The ﬁnal-state electron takes all the neutrino energy (minus the 1.44 MeV

threshold) so the electron energy spectrum yields directly the neutrino spec-

trum. The neutral-current dissociation of

H (8.82) is equally sensitive to

all neutrino species so its rate yields the total ν

ﬂux. The ﬁnal state neu-

trons are identiﬁed through the 6.25 MeV photon emitted after the neutron

is thermalized and then captured on

H →

H γ E

=6.25 MeV . (8.84)

Finally, neutrino-electron elastic scattering (8.83) is primarily sensitive to ν

but also to ν

and ν

with a cross-section about ﬁve times smaller. Even for

the cross-section is about ten times smaller than for (8.81) since the ﬁrst

is proportional to G

∼ G

, while the second is proportional to

with E

∼ 10m

This large amount of heavy water was provided by the Canadian government

who, as explained in Chap. 6, uses heavy water as a neutron moderator in their

nuclear reactors.

Cherenkov light is emitted by particles of velocity greater than the phase velocity

in the medium, c/n where n is the refraction index.

8.4 Nuclear astronomy 385

heavy water

−

Cherenkov

light

light water

photomultipliers

Fig. 8.14. A schematic of the Sudbury Neutrino Observatory (SNO) detector. One

kiloton of heavy water is observed by photomultipliers through a light-water shield.

[The purpose of the shield is to prevent neutrons from entering the heavy water

and simulating the reaction (8.82).] Relativistic particles emit Cherenkov light that

is detected by the photomultipliers. The quantity of light is proportional to the

energy of the relativistic particles. The Cherenkov light is emitted in the forward

direction so direction of the recoil electron can be determined from the pattern of

photomultiplier hits.

The energy spectrum of SNO events is shown in Fig. 8.15 along with the

expectations for the three types of reactions. The angular distribution with

respect to the Sun in the ﬁgure shows the peaking in the forward direction

due to neutrino-electron elastic scattering. These events are forward peaked

because the neutrino energy is much greater than the target mass so the

center-of-mass moves forward in the laboratory. The angular distribution for

charged-current events show a small expected asymmetry due to the weak-

interaction matrix element.

The rates for the three reactions allow one to deduce the ﬂux of ν

neu-

trinos. The neutral-current reactions gives a total ﬂux of [81]

+ φ

=(6.42 ± 1.57 ± 0.58) × 10

−2

−1

, (8.85)

386 8. Nuclear Astrophysics

−.5 0

−

−1.0

7115913

NC+CC+ES

cosθ

E(MeV)

160

120

vents

200

400

vents

Fig. 8.15. The SNO measurement of the solar-neutrino ﬂux from

B β-decay [81].

Most events are due to the charged current (CC) reaction (8.81) and to the neutral

current (NC) reaction (8.82). The top ﬁgure shows the spectrum of event energy

as measured by the quantity of Cherenkov light. The two solid curves show the

distributions expected for (8.81) and (8.82). The bottom ﬁgure shows the direction

of recoil electrons with respect to the direction of the Sun. The peak at small angles

is due to neutrino-electron elastic scattering (ES), (8.83).

8.4 Nuclear astronomy 387

where the ﬁrst and second errors are respectively statistical and systematic.

This is in quite satisfactory agreement with the solar model predictions of

the ﬂux of ν

of (5.0 ± 1.0) × 10

−2

−1

The ﬂux of ν

as determined from the charged-current reaction is [81]

=(1.76 ± 0.06 ± 0.09) × 10

−2

−1

. (8.86)

As expected from the considerations of Chap. 4, the solar ν

have been par-

tially transformed into neutrinos of other species. The number transformed

is consistent with that expected for the presently accepted neutrino masses

and mixing angles (4.139).

The SNO results are consistent with those deduced using the data from

the Super Kamiokande experiment [82]. This experiment is similar to SNO

but uses only light water. As such it is sensitive to ν

only through reaction

(8.83) but has an enormous mass (20 kton) and thus has very small statistical

errors.

Radiochemical detectors. Because of their low energy, the ν

and ν

cannot be easily identiﬁed because electrons produced by such neutrinos can-

not be distinguished from the β-decays due to natural radioactivity. These

solar neutrinos can, however be detected through neutrino absorption

(A, Z) → e

−

(A, Z +1),

if the ﬁnal-state nucleus can be identiﬁed. Generally the nucleus is chemi-

cally separated from the target. For this reason, these experiments are called

radiochemical experiments.

The ﬁrst such experiment was that of R. Davis and collaborators [83] who

used the reaction:

Cl → e

− 37

Ar Q = −814 keV

The threshold for this reaction corresponding to the energy necessary to

produce the ground state of

Ar is 814 keV. Because of this threshold, the

experiment is insensitive to ν

To interpret the Davis results, it is essential to remember that the

nucleus can be produced in an excited state and it is necessary to know

the cross-section for each state. The spectrum of states of

Ar is shown in

Fig. 8.16. The ν

yield only the ground state of

Ar. The cross-section for

this state can be deduced from the lifetime of

Ar since the nuclear matrix

element is the same. The ν

yield many excited states of

Ar but luckily the

nuclear matrix elements for these transitions can be accurately derived from

the rates for the mirror decays

Ca →

∗

−

[83].

The total absorption rate then depends on φ

, φ

,andonφ

other

(CNO

and pep neutrinos). It is traditional to express the rate in “solar neutrino

units” or “SNU’s” (1 SNU = 10

−36

events per target atom per second). The

calculated rate is [73]:



φ(E

)σ(E

)dE

=[5.76

+1.15

+0.7

other

]SNU

388 8. Nuclear Astrophysics

wherewehavenormalizedtheν

ﬂuxes to those calculated by Bahcall [73]:

≡ φ

/φ

(Bahcall), etc. Since SNO has measured

to be 0.35 ± 0.04,

this gives



φ(E

)σ(E

)dE

=[2.01 + 1.15

+0.7

other

]SNU

The rate measured with a chlorine detector can then be used to deduce the

ﬂux of ν

and the CNO/pep neutrinos. If these ν

components are present,

therateshouldbeabout4SNU.

1/2+

5/2+

3/2+

1/2+

5/2+

3/2+

β+

(ν, e−)

3/2+

E (MeV)

Fig. 8.16. The A = 37 nuclei. The states of

Ar populated by neutrino absorp-

tion on

Cl are shown. The weak matrix elements for these transitions can be

determined from the rates for the mirror decays of

Ca to

The Homestake experiment in the Homestake gold mine of Lead, North

Dakota uses 600 tons of C

as the neutrino target. It is shown schemat-

ically in Fig, 8.17. It is contained in a large tank along with about 1 mg of

non-radioactive argon “carrier.” After a three month exposure time, the car-

rier and any

Ar produced by solar neutrinos is extracted from the C

bubbling helium through the tank. The argon is then separated from the he-

lium and trapped in a small proportional counter where the electron-capture

decays of the

Ar (t

1/2

= 37 day) are detected via their Auger electrons.

Over a 25 year period, the three month exposures have yielded, on average

about six detected decays of

Ar. After taking into account the detection

8.4 Nuclear astronomy 389

helium

Argon trap

Fig. 8.17. The principle of the Homestake neutrino experiment.

Ar atoms pro-

duced by neutrino absorption are swept out the the C

by bubbling helium gas

through the liquid. The argon is then separated in a cold trap and introduced into a

small proportional counter where the electron-capture decays of

Ar are observed

eﬃciency, this corresponds to 2.56 ±0.16 SNU [83]. Compared with the SNO-

corrected standard model prediction of 4 SNU, this indicates that the ν

are

also strongly suppressed by neutrino oscillations and/or the MSW eﬀect, as

expected for the estimated values of the neutrino masses and mixing angles

(4.139).

Finally, two experiments, SAGE [85] and GALLEX [84], have observed

solar neutrinos via neutrino absorption on gallium:

Ga → e

− 71

The threshold for this reaction is 233 keV, making the experiment sensitive

to all known sources of solar neutrinos. The ν

yield only the ground state

Ge so the cross section can be calculated from the lifetime of

Ge. The

are also expected to yield primarily the ground state while the ν

yield

a multitude of excited states. The calculated rate is [73]



φ(E

)σ(E

)dE

[69.7

+34.2

+12.1

+12

other

] SNU (8.87)

The coeﬃcient in front of

is accurate only to a factor two but this is of

no great importance in view of the small ﬂux measured by SNO,

=0.35.

The gallium experiments follow rather closely the technique of the chlorine

experiment. The targets are in the form of a liquid (100 tons of GaCl

for

GALLEX and 60 tons of gallium metal for SAGE), and the volatile carrier

(GeCl

) is extracted along with the produced

Ge. The electron capture

390 8. Nuclear Astrophysics

decays of

Ge (t

1/2

=11.43 day) are then observed in small proportional

counters.

GALLEX and SAGE have measured rates of 75 ± 7 SNU. This suggest

that the majority of the ν

are present as ν

, as expected for the present

estimates of the neutrinos masses and mixing angles (4.139).

Conclusions from solar neutrino detection. For many years, the inter-

pretation of solar neutrino experiments was hampered by a lack of indepen-

dent evidence for neutrino masses and oscillations. Now that the Kamland

reactor experiment [48] has seen neutrino oscillations, one has no hesitation

to interpret the rates of solar experiments taking into account the MSW

eﬀect and neutrino oscillations. This has lead to very precise tests of solar

models. One recent paper makes the following comparison between measured

and calculated solar neutrino ﬂuxes [86]

φ(pp)

measured

=(1.02 ± 0.02 ± 0.01) φ(pp)

theory

, (8.88)

φ(

measured

=(0.88 ± 0.04 ± 0.23) φ(

theory

, (8.89)

φ(

Be)

measured

=(0.91

+0.24

−0.62

± 0.11) φ(

Be)

theory

, (8.90)

where the ﬁrst errors are observational and the second are theoretical. If the

excellent agreement between observation and theory survives future improved

measurement of neutrino oscillation parameters, it will conﬁrm a triumph of

experimental and theoretical nuclear astrophysics.

8.4.2 Supernova neutrinos

As explained in Sect. 8.2.3, massive stars may end their lives with a “core-

collapse” supernova in which the

Fe core collapses to a neutron star. Such

events are powerful radiators of all species of neutrinos. The ﬁrst to be cre-

ated are “neutronization” ν

from electron captures transforming protons to

neutrons

−

(A, Z) → ν

(A, Z −1) . (8.91)

While these neutrinos are essential for the production of a neutron star,

the most plentiful neutrinos come from purely thermal process that create

neutrinos through reactions like

γγ ↔ e

−

↔

νν. (8.92)

These reactions are due to the neutral currents and therefore produce all

species of neutrinos. The proto-neutron star is so dense that the neutrinos

do not immediately escape, but rather diﬀuse out just like photons in normal

stars, with the escape time given by (8.25)

τ ∼

σN

, (8.93)

8.4 Nuclear astronomy 391

but now with σ given by the weak interactions rather than σ

. Taking σ =

−45

and R ∼ 10 km, this gives τ ∼ 10 s.

Because their cross-section is so much smaller than that of photons im-

plying a correspondingly shorter escape time, the energy evacuated during

the collapse to a neutron star is almost entirely taken up by the neutrinos.

The total energy was calculated as (8.68)

∆E ∼ (3/5)

∼ 3 × 10

J M =1.5 M



. (8.94)

This energy is expected to be approximately equally divided among the 6

types of neutrinos and antineutrinos.

The neutrinos are expected to have a roughly thermal distribution with

a temperature equal to that of the “neutrinosphere,” the layer of material

where the neutrinos last scattered before escaping. Calculations give diﬀerent

temperatures for the diﬀerent species:

∼ 3.5MeV kT

∼ 5MeV kT

ν=ν

∼ 8 MeV (8.95)

Themeanenergiesare∼ 3kT. The non-electron neutrinos and antineutri-

nos have the highest temperature because they interact only through neu-

tral current interactions. (Their energies are insuﬃcient to create muons or

tauons.) They therefore have the smallest cross-sections and therefore escape

the proto-neutron star from the deepest, hottest depth. The

and ν

have

also charged current interaction so they continue scatter to a greater distance

from the center implying a smaller temperature. The ν

have a higher cross-

section than

because ν

charged-current scatter on the plentiful neutrons

while

charged-current scatter on the rarer protons.

The

from the core-collapse supernovae 1987a in the Large Magellanic

Cloud were observed by the Kamiokande [87] and IMB [88] experiments. Both

experiments were kiloton-scale experiments similar to SNO (Fig. 8.14) except

that they contained only light water. (Kamiokande experiment was an earlier

version of Super-Kamiokande.) The supernova

therefore scattered on the

free protons in the water through the reaction

p → e

n . (8.96)

The ﬁnal state positron creates Cherenkov light as in the SNO experiment.

The energy of the

is deduced from the quantity of light.

The 11

events observed by Kamioka and the 8 events by IMB over a

period of 10 s on February 23, 1987 were suﬃcient to conﬁrm the basic picture

of gravitational collapse with the evacuation of energy by neutrinos. Precision

tests of the scenario will require taking into account neutrino oscillations and

the MSW eﬀect.

Further progress in the ﬁeld of supernova-neutrino astronomy will be dif-

ﬁcult because the total rate of supernova in our galaxy and the nearby Mag-

ellanic Clouds is believed to be about 2 per century. Present detectors are

not large enough to detect supernovae in more distant galaxies.

392 8. Nuclear Astrophysics

It would be very interesting to detect the non-

components of the neu-

trino spectrum. If SNO is still in operation, it will observe the ν

component

through the reaction (8.81) and the other components through (8.82) and

(8.83). Another recently suggested neutral-current detector [89] would use

ν p → ν p . (8.97)

The energy spectrum of the recoil protons would give information on the ν

and ν

energy spectra.

8.4.3 γ-astronomy

γ-astronomy is a vast ﬁeld that observes high-energy photons from a variety

of sources. Many deal with sources related to the production or propagation

of cosmic rays. The recently discovered γ-ray bursts are now suspected to be

related in some way to gravitational-collapse events.

In the context of nuclear physics, the most interesting sources of γ-rays are

radioactive nuclei produced in supernovae and then ejected into interstellar

space. Once the expanding cloud of matter becomes suﬃciently dilute, it

becomes transparent of γ-rays so they become detectable.

Table 8.2 lists the radioactive nuclei that emit γ-rays that have a lifetime

suﬃciently long to be observed. Most are expected to come from supernovae

but some may be ejected in less violent “novae” that are thought to be

superﬁcial explosions on white dwarfs acreting matter from a binary com-

panion. Such novae favor the production of relatively low mass nuclei. Some

radioactive nuclei are expected to be ejected through continuous mass loss

by Wolf-Rayet (WR) and Asymptotic Giant Branch (AGB) stars.

The radioactive decays of the ﬁrst three groups, A = 56, 57 and 44 are

believed to be the major heating source in the expanding clouds around

supernovae. In fact, the luminosities of some supernovae are observed to

decrease with the lifetimes of

Co, then

Co and the

Ti. This is illustrated

in Fig. 8.8. As long as the γ-rays are involved in heating the cloud, it cannot

be entirely transparent, so the expected ﬂux is complicated to calculate.

As shown in Fig. 8.18, the

Co γ-rays were observed from the remnant

of SN1987a and

Ti γ-rays from the supernova remnant Cas A. We see that

the ﬂuxes are just at the limit of detectability for these two nearby remnants.

They nevertheless give strong evidence that radioactive nuclei are, indeed,

ejected by supernovae. Another γ-ray that has been detected is that from

1/2

=7.17 × 10

yr). Its long half-life means that its ﬂux represents the

combined eﬀects of many supernovae. Indeed, a diﬀuse ﬂux of

Al photons

has been detected throughout the galactic plane and gives constraints on the

rate of nucleosynthesis over the last 10

yr.

Gamma-ray observatories now in orbit, especially the INTEGRAL mis-

sion, should greatly increase the amount of signiﬁcant data available.