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Nuclei


Quark Fusion and Hyper-nucleus

The lambda baryon 0 was discovered in 1950. It is one of those hyperons, which carries a strange quark besides 2 of the up/down quarks. All the baryones eventually decay to proton at the lowest mass level (Table 14-07), but the hyperons have a relatively long lifetime of about 2x10-10 sec because of the conservation of the "strangeness" quantum number and only the weak interaction ignores such rule. The charmed lambda c with a charmed in place of the strange was discovered in 1947. This one has a lifetime of about 2x10-13 sec and also decays via the weak interaction only. Charmed baryons are formed in high-energy particle collisions, such as those produced by particle accelerators (see an example in Figure 14-32).
Quark Fusion Binding Energy The doubly charmed xi cc++ was discovered only recently on July 2017 at LHCb (see the article by "PhysicsWorld"), its lifetime is estimated to be about 10-13 sec. Further works found that there is a net energy of 12 Mev released in its formation (see another article in "Phys.Org"). Subsequent calculations show that the energy released can be up to 138 Mev if the 2 charmed quarks are replaced by 2 bottom quarks (see generalized formula, illustration and table in Figures 14-31, 14-32). Such amount of energy is similar to (and exceeded) the fusion reactions such as D + T He + n + 17.6 Mev.

Figure 14-31 Quark Fusion [view large image]


Figure 14-32 Binding Energy [view large image]


Unfortunately (or fortunately) the short lifetime of c prevents the initiation of chain reaction (in making bomb for example). Hyperons is expected to be present in the core of neutron star at density ~ 1015 gm/cm3, so that the rate of production ~ decay rate.


Hyper-nucleus Just like a Russian Doll, there is another layer of the nuclear structure, which contains one or more hyperons or other heavy baryons in the atomic nucleus. This is called hyper-nucleus with the symbol : AQZ, where A is the number of nucleons (protons + neutrons) in the nucleus, Z the atomic number (or its symbol), and Q the hyperon or other heavy baryon (number of Q could be more than 1), then the number of neutron n = A - Z - k (at present time k is mostly equal to 1, at most 2, see Figure 14-33). The corresponding binding energy BQ = Mcore + MQ - Mhyp, where Mcore is mass of A-1Z, MQ mass of the Q baryon, and Mhyp mass of the hypernucleus AQZ. For example, the carbon nucleus with 1 hyperon replacement for a neutron would be labeled as 12C.

Figure 14-33 Hyper-nucleus
[view large image]

Hyper-nucleus can be produced, for example, by the reaction :
K-(ũs) + nucleus [core, n(udd)] -(ũd) + hyper-nucleus [core, (uds)], where ũ = anti-u.

Until recently in 2017, experimental studies of hyper-nucleus were performed mostly on elements of low atomic number with the replacement by one baryon. As shown in Figure 14-34, all of them increase the binding energy of the nucleus like adding more glue to keep the components together. Theoretical calculations on elements of higher atomic number also arrive at the same conclusion. Figure 14-35 plots the binding energy per nucleon
Binding Energy Binding Energy per A (BE/A) for some elements from Z = 28 and beyond. It shows the upward trend of BE/A as the number of replacement increases. The small insert in the same diagram portrays the increment in BE/A as the number of replacement increases. In regular BE/A plot 56Fe is at the peak, which is now superseded by 60+8Ni. It seems that we can make more powerful nuclear bomb by adding more baryons into the nucleus. Fortunately, the scheme is foiled by the short lifetime of about 10-10 sec.

Figure 14-34 Binding Energy [view large image]

Figure 14-35 Binding Energy / A

The latest research on hyper-nucleus goes beyond the to the one involving bottom quarks such as those in the reaction : .
It is estimated that the energy released in this reaction would be about 300 Mev, i.e., ~ 1.5 time to that from 235U fission. It is rather fortunate again that such reaction is extremely difficult to achieve even experimentally due to the short lifetime (~ 1.6x10-12 sec) of B- (see Table 14-08).

Although the higher binding energy in hyper-nucleus is useless, the hyperon now inside the nucleus can be used to investigate the nuclear structure such as the detail of the single particle shell model. This is related to its additional strange quantum number, which allows more freedom to move around without the restriction of the Pauli Exclusion Principle (see "Single-Particle Potentials and Effective Masses of Hyperons in Hyperonic Nuclear Systems").

List of Baryons

Table 14-07 List of Baryons [view large image] (from Wikipedia)

Symbols : I (isospin), J (total angular momentum), P (parity), u (up quark), d (down quark), s (strange quark), c (charm quark), b (bottom quark), Q (charge), S (strangeness), C (charm), B' (bottomness).

List of Mesons

Table 14-08 List of Mesons [view large image] (from Wikipedia)

List of elementary particles :


See the latest (2017) research in "Quark-level Analogue of Nuclear Fusion with Doubly Heavy Baryons".

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