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Supernova neutrino detection
Nuclear Physics B (Proc. Suppl.) 145 (2005) 339–342 www.elsevierphysics.com
Supernova neutrino detection M. Selvia a
Bologna University and INFN, via Irnerio, 46, 40126, Bologna, Italy Neutrinos emitted during a supernova core collapse represent a unique feature to study both stellar and neutrino properties. After discussing the details of the neutrino emission in the star and the effect of neutrino oscillations on the expected neutrino fluxes at Earth, a review of the detection techniques is presented in this paper, with particular attention to the problem of electron neutrino detection.
1. Supernova neutrino emission At the end of its burning phase a massive star (M ≥ 8M ) explodes into a supernova (SN), originating a neutron star which cools emitting about 99 % of the liberated gravitational binding energy in neutrinos: Eb 3 · 1053 erg. The time-integrated spectra can be well approximated by the pinched Fermi–Dirac distribution, with an effective degeneracy parameter η. For the neutrino of flavor α, we have Fα0 =
Lα E2 4πD2 Tα4 F3 (ηα ) eE/Tα −ηα + 1
(1)
where D is the distance to the supernova, E is the ν energy, Lα is the luminosity of the flavor να , and Tα represents the effective temperature of the ∞να gas inside the neutrinosphere, F3 (ηα ) ≡ 0 x3 /(ex−ηα + 1) dx is the normalization factor. Due to the different trapping processes, the different neutrino flavors originate in layers of the supernova with different temperatures. The electron (anti)neutrino flavor is kept in thermal equilibrium by β processes up to a certain radius usually referred to as the “neutrinosphere”, beyond which the neutrinos stream off freely. However, the practical absence of muons and taus in the supernova core implies that the other two neutrino flavors, here collectively denoted by νx (νµ , ντ , ν¯µ , ν¯τ ), interact primarily by less efficient neutral-current processes. Therefore, their spectra are determined at deeper, i.e. hotter, regions. In addition, since the content of neu0920-5632/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2005.04.035
trons is larger than that of protons, νe escape from outer regions than ν¯e . This rough picture leads to the hierarchy Eνe < Eν¯e < Eνx . Typical ranges for the average energies of the time-integrated neutrino spectra obtained in simulations are Eνe = 10−12 MeV, Eν¯e = 11−17 MeV, and Eνx = 15 − 24 MeV [1,2]. However, recent studies with an improved treatment of ν transport, microphysics, the inclusion of the nucleon bremsstrahlung, and the energy transfer by recoils, find somewhat smaller differences between the ν¯e and νx spectra [3]. The amount of the total binding energy Eb taken by each flavor is Lα = fνα Eb , with fνe = 17 − 22%, fν¯e = 17 − 28%, fνx = 16 − 12%. Thus, the so-called “energy equipartition” has to be intended as “within a factor of two” or so [4]. Typical neutrino energy spectra at the generation inside the star are shown in Figure 1. 2. Effect of neutrino oscillation In the study of SN neutrinos, νµ and ντ are indistinguishable, both in the star and in the detector because of the corresponding charged lepton production threshold; consequently, in the frame of three-flavor oscillations, the relevant parame2 2 ) and (∆m2atm , Ue3 ). ters are just (∆m2sol , Ue2 We will adopt the following numerical values: ∆m2sol = 7 · 10−5 eV2 , ∆m2atm = 2.5 · 2 10−3 eV2 , Ue2 = 0.33; the selected solar parame2 2 ) describe the LMA-I solution, as ters (∆msol , Ue2 it results from a global analysis including solar,
340
M. Selvi / Nuclear Physics B (Proc. Suppl.) 145 (2005) 339–342
for normal hierarchy and Fe
2 = Ue2 Fe0
Fe¯ =
Figure 1. Neutrino energy spectra at the neutrinosphere. CHOOZ and KamLAND ν data [5]. For a normal mass hierarchy (NH) scheme, ν (not ν¯) cross two resonance layers: one at higher 2 , density (H), which corresponds to ∆m2atm , Ue3 and the other at lower density (L), corresponding 2 . For inverted mass hierarchy (IH), to ∆m2sol , Ue2 transitions at the higher density layer occur in the ν¯ sector, while at the lower density layer they occur in the ν sector. Given the energy range of SN ν (up to ∼ 100 MeV) and considering a star density profile ρ ∝ 1/r3 , the adiabaticity condition is always satisfied at the L resonance for any LMA solution, while at the H resonance, this depends on the 2 in the following way: value of Ue3 2 (∆m2atm /E)2/3 ] PH ∝ exp [const Ue3
where PH is the flip probability between two adjacent mass eigenstates. 2 ≥ 5 · 10−4 the conversion is comWhen Ue3 pletely adiabatic, meaning that the flip proba2 bility is null (PH = 0); conversely, when Ue3 ≤ 5 · 10−4 the conversion is completely non adiabatic, meaning that the flip probability is PH = 1. The oscillation scheme can be summarized as: 2 Fe0 Fe= PH Ue2 2 Fe¯0 Fe¯ = Ue1
+ +
2 (1 − PH Ue2 ) 2 0 Ue2 Fx¯
Fx0
(2) (3)
2 PH Ue1
Fe¯0
2 + Ue1 Fx0
+ (1 −
2 PH Ue1 )
(4) Fx¯0
(5)
for inverted hierarchy, 0 are the original neutrino fluxes in the where Fany star and Fany are the observed ν fluxes. One can notice that, in the antineutrino channel, the non adiabatic (PH = 1), IH case, is equivalent to the NH case (which does not depend on adiabaticity). If we consider the effect of Earth in the neutrino path to the detector, we must replace, in the de2 with Pei (i = 1, 2), tected flux estimation, Uei the probability for the mass eigenstate νi to be detected as νe after path in the Earth [6], which depends on the solar oscillation parameters and on the travelled density profile through the Earth. 3. Parameter estimation The number of parameters involved in the calculation of the expected ν rate from a SN core collapse is very large. They can be subdivided in astrophysical (Eb , Tα , fα , ηα with α = νe , ν¯e , νx ) and related to neutrino physics (θ12 , PH (θ13 ), sign of ∆m213 ). There are two possible approaches: the first one is to perform a global fit to the data, determining both astrophysical and oscillation parameters. There are degeneracies, so that different parameter variations can produce the same observable effects. This method is followed in [7]. The other one (which seems more promising) is to perform an analysis on ratios of both νe and ν¯e observables, such as the ratio of the average neutrino energies or the widths of the energy distributions, as proposed in [8]. Therefore one of the main goals of future SN ν detectors is the possibility to detect a high number of electron neutrinos in addition to the, already large, sample of ν¯e . 4. The “standard” detection techniques In Table 1 a list of the detectors, suitable for SN ν, and presently in data acquisition is shown.
M. Selvi / Nuclear Physics B (Proc. Suppl.) 145 (2005) 339–342
Table 1 Supernova neutrino detectors presently in data acquisition. Detector Mass (t) Target Super-Kamiokande 32000 H2 O SNO 1400, 1000 H2 O,D2 O KamLAND 1000 Cn H2n LVD 1000 Cn H2n MiniBoone 500 Cn H2n BUST 330 Cn H2n
341
Technique Water Cerenkov Heavy water Cerenkov Liquid scintillator “ “ “
Other approved detectors in construction: Borexino (300 t of C9 H12 ), Icarus (600 t of liquid Ar). 5. Some new ideas in the market Here we present an “uncoherent” list of the most recent new ideas to improve the existing SN ν detectors or to find alternative ways for ν detection. 5.1. Gd-doped water Cherenkov detectors Adding a small amount of Gadolinium (100 t of GdCl3 in SK) a water Cerenkov detector can greatly enhance its performances [9]. The high Gd neutron capture cross section allows to get about 90% of the neutrons produced in the inverse beta decay interaction (¯ νe + p → n + e+ ), detecting a photon cascade with ΣEγ 8 M eV . For the SN ν detection there are improvements in the following areas: S/N ratio, the deconvolution of the various neutrino signals, elastic scattering pointing accuracy, νe detection through the νe +16 O →16 F + e− interactions, the SN relic ν and the possibility to get a SN prealarm through the detection of the ν emitted during the silicon burning phase, about 2 days before the SN [10]. 5.2. Detection of the ν p → ν p elastic scattering In [11] the authors proposed that ν p elastic scattering can be used for the detection of SN ν in liquid scintillator detectors. The number of detectable events is critically dependent on the detector energy threshold because the proton recoil kinetic energy spectrum is soft and, moreover, the scintillation light from slow, heavily ionizing protons is quenched. For example the expected number of detected events in Kamland, with an
assumed 200 keV energy threshold, for a “standard” SN is ∼ 300. In addition, the measured proton spectrum is related to the incident ν spectrum. This is not true for other NC interaction νi + d → νi + p + n and νi +12 C → νi +12 C + γ where the detected signals are monoenergetic. Remember that NC are the only way to measure non-electron SN ν, so the ν p elastic scattering allows to measure separately their temperature and fraction of energy. 5.3. New generation very large liquid scintillator detectors There are some ideas [12], although embryonal, about the possibility to build a very large liquid scintillator detector. The mass scale could be about a factor 30 with respect to the largest detector presently running (LVD and KamLand). Beyond the obvious scaling in the number of expected events, the idea is intriguing for the following topics: - the detection of the previously mentioned ν p elastic scattering (if the threshold is low enough), - the possibility to measure Earth matter effects with a single detector, as proposed in [13], thanks to the very good energy resolution - and the possibility to detect, with high statistic, the νe 12 C,12 N e− and ν¯e 12 C,12 B e+ interactions and to statistically distinguish between them, measuring the time and energy distribution of the 12N and 12B beta decay products, as shown in [14]. 5.4. Detection of the νe 40 Ar interaction A liquid argon TPC has the ability to detect SN ν through 3 processes: elastic scattering by
342
M. Selvi / Nuclear Physics B (Proc. Suppl.) 145 (2005) 339–342
electrons (all ν species), νe ( ν¯e ) CC interaction on Ar with production of excited K (Cl). The estimated number of events for a “standard” SN in the 3 kt ICARUS detector is about 200 ÷ 250, where the main part comes from the νe -Ar interaction [15]. Due to the high sensitivity to νe , ICARUS is in principle sensitive to the νe breakout burst in the first tens of ms after the bounce. 5.5. Detection of the ν 56 F e interaction The ν CC interaction with iron nuclei νe 56 Fe,56 Co e− can be efficiently used for the detection of SN ν. The cross section is larger than the inverse beta decay one for Eν > 20 M eV . The key point is the evaluation of the efficiency for the produced charged lepton to escape from iron and leave energy in the active detectors. In the LVD detectors (liquid scintillator embedded in many thin (∼ 1 cm) iron tanks) the contribution of ν-Fe interactions can be as high as about 20% of the total rate [16], as shown in Figure 2. As a reference example, in the largest iron ν detector (MINOS, 5.4 kt), the estimated number of events is about 1000, where we consider those events for which the lepton can escape iron and release energy in the scintillator bars. Of course the real number of detectable events is related to the trigger and the noise in the single bar, which we cannot estimate. 5.6. Detection of the νe 56 P b interaction ADONIS [17] is a project, under study in the USA, to build a detector made of thin lead layers interleaved with plastic scintillators. The order of magnitude is about 500 t of lead. The basic idea is that the νe -Pb cross section is about 100 times larger than the ν¯e -Pb one, thus it is possible to select a very clean νe sample. A key point for this kind of detectors is its energy resolution, deeply related to its sampling. Also neutral current interactions can be studied thanks to the large number of neutrons produced. REFERENCES 1. H. T. Janka, Vulcano Workshop 1992 Proceedings, 345-374, (1992). 2. T. Totani et al., Astrophys. J. 496, 216 (1998). (astro-ph/9710203)
Figure 2. Impact of iron interactions in the SN neutrino signal in LVD. 3. M. T. Keil et al., Astrophys. J. 590, 971 (2003). (astro-ph/0208035) 4. F. Cavanna et al., Surveys High Energ.Phys. 19, 35 (2004). (astro-ph/0311256) 5. G. L. Fogli et al., Phys. Rev. D67, 073002 (2003). (hep-ph/0212127) 6. C. Lunardini, A. Yu. Smirnov, Nucl. Phys. B616, 307 (2001). (hep-ph/0106149) 7. V. Barger et al., Phys. Lett. B547, 37 (2002). (hep-ph/0112125) 8. C. Lunardini, A. Yu. Smirnov, JCAP 06, 009 (2003). (hep-ph/0302033) 9. J. Beacom and M. Vagins, hep-ph/0309300. 10. A. Odrzywolek et al., astro-ph/0311012. 11. J. Beacom et al., hep-ph/0205220. 12. L. Oberauer et al., http://axpd24.pd.infn.it/ NO-VE/transparencies/oberauer.ppt 13. A. Dighe et al., JCAP 06, 006 (2003). (hepph/0304150) 14. see http://www.ba.infn.it/∼now2004/talks/ 17 09 04/par/Selvi.ppt and LVD collaboration, paper in preparation. 15. I. Botella et al., hep-ph/0307222 and hepph/0307244. 16. LVD collaboration, Proc. 28 ICRC, Tsukuba, 1297 (2003). (hep-ph/0307287) 17. see http://gate.hep.anl.gov/rlt/ADONIShome/ADONIS-home index.html
Supernova neutrino detection M. Selvia a
Bologna University and INFN, via Irnerio, 46, 40126, Bologna, Italy Neutrinos emitted during a supernova core collapse represent a unique feature to study both stellar and neutrino properties. After discussing the details of the neutrino emission in the star and the effect of neutrino oscillations on the expected neutrino fluxes at Earth, a review of the detection techniques is presented in this paper, with particular attention to the problem of electron neutrino detection.
1. Supernova neutrino emission At the end of its burning phase a massive star (M ≥ 8M ) explodes into a supernova (SN), originating a neutron star which cools emitting about 99 % of the liberated gravitational binding energy in neutrinos: Eb 3 · 1053 erg. The time-integrated spectra can be well approximated by the pinched Fermi–Dirac distribution, with an effective degeneracy parameter η. For the neutrino of flavor α, we have Fα0 =
Lα E2 4πD2 Tα4 F3 (ηα ) eE/Tα −ηα + 1
(1)
where D is the distance to the supernova, E is the ν energy, Lα is the luminosity of the flavor να , and Tα represents the effective temperature of the ∞να gas inside the neutrinosphere, F3 (ηα ) ≡ 0 x3 /(ex−ηα + 1) dx is the normalization factor. Due to the different trapping processes, the different neutrino flavors originate in layers of the supernova with different temperatures. The electron (anti)neutrino flavor is kept in thermal equilibrium by β processes up to a certain radius usually referred to as the “neutrinosphere”, beyond which the neutrinos stream off freely. However, the practical absence of muons and taus in the supernova core implies that the other two neutrino flavors, here collectively denoted by νx (νµ , ντ , ν¯µ , ν¯τ ), interact primarily by less efficient neutral-current processes. Therefore, their spectra are determined at deeper, i.e. hotter, regions. In addition, since the content of neu0920-5632/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2005.04.035
trons is larger than that of protons, νe escape from outer regions than ν¯e . This rough picture leads to the hierarchy Eνe < Eν¯e < Eνx . Typical ranges for the average energies of the time-integrated neutrino spectra obtained in simulations are Eνe = 10−12 MeV, Eν¯e = 11−17 MeV, and Eνx = 15 − 24 MeV [1,2]. However, recent studies with an improved treatment of ν transport, microphysics, the inclusion of the nucleon bremsstrahlung, and the energy transfer by recoils, find somewhat smaller differences between the ν¯e and νx spectra [3]. The amount of the total binding energy Eb taken by each flavor is Lα = fνα Eb , with fνe = 17 − 22%, fν¯e = 17 − 28%, fνx = 16 − 12%. Thus, the so-called “energy equipartition” has to be intended as “within a factor of two” or so [4]. Typical neutrino energy spectra at the generation inside the star are shown in Figure 1. 2. Effect of neutrino oscillation In the study of SN neutrinos, νµ and ντ are indistinguishable, both in the star and in the detector because of the corresponding charged lepton production threshold; consequently, in the frame of three-flavor oscillations, the relevant parame2 2 ) and (∆m2atm , Ue3 ). ters are just (∆m2sol , Ue2 We will adopt the following numerical values: ∆m2sol = 7 · 10−5 eV2 , ∆m2atm = 2.5 · 2 10−3 eV2 , Ue2 = 0.33; the selected solar parame2 2 ) describe the LMA-I solution, as ters (∆msol , Ue2 it results from a global analysis including solar,
340
M. Selvi / Nuclear Physics B (Proc. Suppl.) 145 (2005) 339–342
for normal hierarchy and Fe
2 = Ue2 Fe0
Fe¯ =
Figure 1. Neutrino energy spectra at the neutrinosphere. CHOOZ and KamLAND ν data [5]. For a normal mass hierarchy (NH) scheme, ν (not ν¯) cross two resonance layers: one at higher 2 , density (H), which corresponds to ∆m2atm , Ue3 and the other at lower density (L), corresponding 2 . For inverted mass hierarchy (IH), to ∆m2sol , Ue2 transitions at the higher density layer occur in the ν¯ sector, while at the lower density layer they occur in the ν sector. Given the energy range of SN ν (up to ∼ 100 MeV) and considering a star density profile ρ ∝ 1/r3 , the adiabaticity condition is always satisfied at the L resonance for any LMA solution, while at the H resonance, this depends on the 2 in the following way: value of Ue3 2 (∆m2atm /E)2/3 ] PH ∝ exp [const Ue3
where PH is the flip probability between two adjacent mass eigenstates. 2 ≥ 5 · 10−4 the conversion is comWhen Ue3 pletely adiabatic, meaning that the flip proba2 bility is null (PH = 0); conversely, when Ue3 ≤ 5 · 10−4 the conversion is completely non adiabatic, meaning that the flip probability is PH = 1. The oscillation scheme can be summarized as: 2 Fe0 Fe= PH Ue2 2 Fe¯0 Fe¯ = Ue1
+ +
2 (1 − PH Ue2 ) 2 0 Ue2 Fx¯
Fx0
(2) (3)
2 PH Ue1
Fe¯0
2 + Ue1 Fx0
+ (1 −
2 PH Ue1 )
(4) Fx¯0
(5)
for inverted hierarchy, 0 are the original neutrino fluxes in the where Fany star and Fany are the observed ν fluxes. One can notice that, in the antineutrino channel, the non adiabatic (PH = 1), IH case, is equivalent to the NH case (which does not depend on adiabaticity). If we consider the effect of Earth in the neutrino path to the detector, we must replace, in the de2 with Pei (i = 1, 2), tected flux estimation, Uei the probability for the mass eigenstate νi to be detected as νe after path in the Earth [6], which depends on the solar oscillation parameters and on the travelled density profile through the Earth. 3. Parameter estimation The number of parameters involved in the calculation of the expected ν rate from a SN core collapse is very large. They can be subdivided in astrophysical (Eb , Tα , fα , ηα with α = νe , ν¯e , νx ) and related to neutrino physics (θ12 , PH (θ13 ), sign of ∆m213 ). There are two possible approaches: the first one is to perform a global fit to the data, determining both astrophysical and oscillation parameters. There are degeneracies, so that different parameter variations can produce the same observable effects. This method is followed in [7]. The other one (which seems more promising) is to perform an analysis on ratios of both νe and ν¯e observables, such as the ratio of the average neutrino energies or the widths of the energy distributions, as proposed in [8]. Therefore one of the main goals of future SN ν detectors is the possibility to detect a high number of electron neutrinos in addition to the, already large, sample of ν¯e . 4. The “standard” detection techniques In Table 1 a list of the detectors, suitable for SN ν, and presently in data acquisition is shown.
M. Selvi / Nuclear Physics B (Proc. Suppl.) 145 (2005) 339–342
Table 1 Supernova neutrino detectors presently in data acquisition. Detector Mass (t) Target Super-Kamiokande 32000 H2 O SNO 1400, 1000 H2 O,D2 O KamLAND 1000 Cn H2n LVD 1000 Cn H2n MiniBoone 500 Cn H2n BUST 330 Cn H2n
341
Technique Water Cerenkov Heavy water Cerenkov Liquid scintillator “ “ “
Other approved detectors in construction: Borexino (300 t of C9 H12 ), Icarus (600 t of liquid Ar). 5. Some new ideas in the market Here we present an “uncoherent” list of the most recent new ideas to improve the existing SN ν detectors or to find alternative ways for ν detection. 5.1. Gd-doped water Cherenkov detectors Adding a small amount of Gadolinium (100 t of GdCl3 in SK) a water Cerenkov detector can greatly enhance its performances [9]. The high Gd neutron capture cross section allows to get about 90% of the neutrons produced in the inverse beta decay interaction (¯ νe + p → n + e+ ), detecting a photon cascade with ΣEγ 8 M eV . For the SN ν detection there are improvements in the following areas: S/N ratio, the deconvolution of the various neutrino signals, elastic scattering pointing accuracy, νe detection through the νe +16 O →16 F + e− interactions, the SN relic ν and the possibility to get a SN prealarm through the detection of the ν emitted during the silicon burning phase, about 2 days before the SN [10]. 5.2. Detection of the ν p → ν p elastic scattering In [11] the authors proposed that ν p elastic scattering can be used for the detection of SN ν in liquid scintillator detectors. The number of detectable events is critically dependent on the detector energy threshold because the proton recoil kinetic energy spectrum is soft and, moreover, the scintillation light from slow, heavily ionizing protons is quenched. For example the expected number of detected events in Kamland, with an
assumed 200 keV energy threshold, for a “standard” SN is ∼ 300. In addition, the measured proton spectrum is related to the incident ν spectrum. This is not true for other NC interaction νi + d → νi + p + n and νi +12 C → νi +12 C + γ where the detected signals are monoenergetic. Remember that NC are the only way to measure non-electron SN ν, so the ν p elastic scattering allows to measure separately their temperature and fraction of energy. 5.3. New generation very large liquid scintillator detectors There are some ideas [12], although embryonal, about the possibility to build a very large liquid scintillator detector. The mass scale could be about a factor 30 with respect to the largest detector presently running (LVD and KamLand). Beyond the obvious scaling in the number of expected events, the idea is intriguing for the following topics: - the detection of the previously mentioned ν p elastic scattering (if the threshold is low enough), - the possibility to measure Earth matter effects with a single detector, as proposed in [13], thanks to the very good energy resolution - and the possibility to detect, with high statistic, the νe 12 C,12 N e− and ν¯e 12 C,12 B e+ interactions and to statistically distinguish between them, measuring the time and energy distribution of the 12N and 12B beta decay products, as shown in [14]. 5.4. Detection of the νe 40 Ar interaction A liquid argon TPC has the ability to detect SN ν through 3 processes: elastic scattering by
342
M. Selvi / Nuclear Physics B (Proc. Suppl.) 145 (2005) 339–342
electrons (all ν species), νe ( ν¯e ) CC interaction on Ar with production of excited K (Cl). The estimated number of events for a “standard” SN in the 3 kt ICARUS detector is about 200 ÷ 250, where the main part comes from the νe -Ar interaction [15]. Due to the high sensitivity to νe , ICARUS is in principle sensitive to the νe breakout burst in the first tens of ms after the bounce. 5.5. Detection of the ν 56 F e interaction The ν CC interaction with iron nuclei νe 56 Fe,56 Co e− can be efficiently used for the detection of SN ν. The cross section is larger than the inverse beta decay one for Eν > 20 M eV . The key point is the evaluation of the efficiency for the produced charged lepton to escape from iron and leave energy in the active detectors. In the LVD detectors (liquid scintillator embedded in many thin (∼ 1 cm) iron tanks) the contribution of ν-Fe interactions can be as high as about 20% of the total rate [16], as shown in Figure 2. As a reference example, in the largest iron ν detector (MINOS, 5.4 kt), the estimated number of events is about 1000, where we consider those events for which the lepton can escape iron and release energy in the scintillator bars. Of course the real number of detectable events is related to the trigger and the noise in the single bar, which we cannot estimate. 5.6. Detection of the νe 56 P b interaction ADONIS [17] is a project, under study in the USA, to build a detector made of thin lead layers interleaved with plastic scintillators. The order of magnitude is about 500 t of lead. The basic idea is that the νe -Pb cross section is about 100 times larger than the ν¯e -Pb one, thus it is possible to select a very clean νe sample. A key point for this kind of detectors is its energy resolution, deeply related to its sampling. Also neutral current interactions can be studied thanks to the large number of neutrons produced. REFERENCES 1. H. T. Janka, Vulcano Workshop 1992 Proceedings, 345-374, (1992). 2. T. Totani et al., Astrophys. J. 496, 216 (1998). (astro-ph/9710203)
Figure 2. Impact of iron interactions in the SN neutrino signal in LVD. 3. M. T. Keil et al., Astrophys. J. 590, 971 (2003). (astro-ph/0208035) 4. F. Cavanna et al., Surveys High Energ.Phys. 19, 35 (2004). (astro-ph/0311256) 5. G. L. Fogli et al., Phys. Rev. D67, 073002 (2003). (hep-ph/0212127) 6. C. Lunardini, A. Yu. Smirnov, Nucl. Phys. B616, 307 (2001). (hep-ph/0106149) 7. V. Barger et al., Phys. Lett. B547, 37 (2002). (hep-ph/0112125) 8. C. Lunardini, A. Yu. Smirnov, JCAP 06, 009 (2003). (hep-ph/0302033) 9. J. Beacom and M. Vagins, hep-ph/0309300. 10. A. Odrzywolek et al., astro-ph/0311012. 11. J. Beacom et al., hep-ph/0205220. 12. L. Oberauer et al., http://axpd24.pd.infn.it/ NO-VE/transparencies/oberauer.ppt 13. A. Dighe et al., JCAP 06, 006 (2003). (hepph/0304150) 14. see http://www.ba.infn.it/∼now2004/talks/ 17 09 04/par/Selvi.ppt and LVD collaboration, paper in preparation. 15. I. Botella et al., hep-ph/0307222 and hepph/0307244. 16. LVD collaboration, Proc. 28 ICRC, Tsukuba, 1297 (2003). (hep-ph/0307287) 17. see http://gate.hep.anl.gov/rlt/ADONIShome/ADONIS-home index.html