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TABLE OF PROPERTIES OF ELEMENTARY PARTICLES*)
A. M. Shapiro
From 1949 to 1954 no fewer than nine different \(K\)-mesons\(^{1}\), or decay schemes of these particles, and no fewer than four different hyperons (\(Y\)-particles) were discovered. Although during the past year no new hyperons or mesons have been found, it has nevertheless been possible to establish many properties of the already known particles. A table of the properties of \(K\)-mesons and hyperons is needed both by specialists in the field of “elementary particles” and by nonspecialists.
The present table has been made as complete and up to date as possible; however, in compiling it no attempt was made to carry out a detailed analysis of each experiment\(^{2}\). The table is intended for use in the laboratory or in teaching; lack of time prevented a detailed re-examination of the data. The principal journals in this field were examined very carefully up to February 1956, but, despite this, only a minimal number of references is given. The numerical values cited often represent approximately weighted data from many experimental measurements; references, however, are given only to one or two papers. This does not mean that experiments not cited are doubtful: the references given are either to the most recent, or to the most accurate, papers, or to papers containing a complete summary of the data. Practically all references to other experiments can be found in the literature cited.
The article contains no detailed analysis of the experimental data and their interrelations. These questions are covered in several excellent reviews and reports delivered at conferences\(^{3}\).
EXPLANATORY REMARKS
In Sections I and II of the table, only those particles are included that have been thoroughly investigated by more than one group of experimenters. Section III includes particles that have not been so well studied
*) Reviews of Modern Physics, vol. 28, No. 2, April 1956, translated from English.
particles and particles whose existence is expected on the basis of theoretical considerations.
Of course, even particles whose existence has been reliably established may have individual properties that have not been sufficiently investigated. This is indicated in the table by parentheses placed in the corresponding places. To denote uncertainty in the data, a question mark is sometimes used. For example, it is known that negative \(K\)-mesons exist, but it cannot be said definitely which of the \(K^{+}\)-particles listed in Section II (and perhaps all of them) have negative antiparticles \(^{\ddagger}\)*). This uncertainty is indicated by placing the minus sign in parentheses in each case.
The mass of the \(\pi\)-meson is of very great importance for the entire table. Thus, for example, the masses of all hyperons given in the table have been obtained by adding the measured decay energies (the values \(Q\)) to the masses of the secondary particles, among which in each case there is a \(\pi\)-meson. In the table, for the mass of the charged \(\pi\)-meson the value \(273.1 \pm 0.2\,m_e\) is used. It is assumed that the \(\pi^{+}\)- and \(\pi^{-}\)-mesons have equal masses. This value is the weighted mean of the values \(273.4 \pm 0.2\,m_e\) and \(272.5 \pm 0.3\,m_e\), obtained for \(\pi^{+}\)- and \(\pi^{-}\)-mesons respectively by Smith, Birnbaum, and Barkas \(^{4}\). After the compilation of the table, a report by Barkas, Birnbaum, and Smith \(^{5}\) was published, containing the values \(273.3 \pm 0.2\,m_e\) and \(272.8 \pm 0.3\,m_e\) for positively and negatively charged mesons. To these should also be added the measurements of Grove and Phillips \(^{6}\), which gave for the mass of the \(\pi\)-meson the value \(272.7 \pm 0.3\,m_e\). Since the new weighted value differs little from the value \(273.1 \pm 0.2\,m_e\), the latter has been retained in the table.
Many experimenters use somewhat different values for the mass of the charged \(\pi\)-mesons, and this explains part of the scatter in the values they obtain for the masses of hyperons and \(K\)-mesons. Obviously it would be better if all authors used a single value of the mass, and we propose as such a value
\(273.1 \pm 0.2\,m_e\).
SECTION I
PARTICLES WHOSE EXISTENCE HAS BEEN RELIABLY ESTABLISHED
A. GROUPING OF PARTICLES
The eighteen elementary particles given in Section I (counting separately the positively and negatively charged ones) are divided into five groups \(^{1}\). The first group includes particles whose mass
*) See the proof-correction notes. This sign (\(\ddagger\)), used below, indicates additional information contained at the end of the article in the “proof-correction notes.”
rest masses of which are less than or equal to the rest mass of the electron. The remaining groups are defined as follows:
\[ L\text{-mesons:}\quad m_e < m_{L\text{-meson}} < m_{\pi^\pm} \]
\[ K\text{-mesons:}\quad m_{\pi^\pm} < m_{K\text{-meson}} < m_{\text{proton}} \]
\[ \text{Nucleons:}\quad \text{proton and neutron} \]
\[ \text{Hyperons:}\quad m_{\text{neutron}} < m_{\text{hyperon}} < m_{\text{deuteron}} \]
The sixth group, consisting of the “non-elementary” deuteron, triton, and \(\mathrm{He}^3\), is included in order to indicate the binding energies and magnetic moments of small formations made up of nucleons.
B. ERRORS
If the positive and negative errors associated with a given number are equal, they are placed in parentheses under those significant digits which are uncertain. If the errors are unequal, the positive errors are placed in parentheses above, and the negative errors below, the corresponding significant digits. For example,
\[ -\,1.001146 \pm 0.000012 \quad \text{is denoted}\quad -\,1.001146, \tag{4} \]
\[ \tag{12} \]
and the quantity
\[ \left(1.3^{+0.4}_{-0.3}\right)\cdot 10^{-10} \quad \text{is denoted}\quad 1.3\cdot 10^{-10}. \tag{3} \]
The errors given are, unfortunately, a mixture of standard deviations and probable errors. Since most authors do not indicate which measure of error they use, great caution is required in estimating the errors given in the most precise experiments.
C. REFERENCES
In Section I of the table, references are indicated by small letters of the Latin alphabet placed to the right of the corresponding tabulated value, beside it or below it. The reference letter is usually placed next to the value; in those cases where the value contains a power of ten, the reference letter is lowered so that it cannot be confused with the exponent.
For brevity, so as not to encumber the text of the table, references are not given in columns 6, 12, 13, and 14 of the table, and in columns 9 and 11 only one reference is given. The sources of the data presented in these columns can be found in the works cited in \(^3\). The establishment of decay schemes and their verification, as well as the determination of the quantum properties of particles, constitute the most important part of research in this area.
In the case of unstable particles, either the mass of the primary particle is measured and the value \(Q\) for the decay is determined from the known mas-
the secondary particles, or the quantity \(Q\) is measured and the mass of the primary particle is obtained from the value of \(Q\) plus the known masses of the secondary particles arising in the decay. In all cases the reference letter is always placed next to the measured quantity. The absence of a reference for the remaining quantities indicates that they have not been measured, but calculated.
D. CONTENTS OF THE COLUMNS AND REMARKS
Column 1
This column gives the commonly used designations of the particles and their charges. The charge is indicated in the upper right corner of each designation. The designations of particles that are definitely not elementary are enclosed in parentheses.
Columns 2, 3, 4, and 5
These columns contain the particle masses in the specified units. In column 5, strictly speaking, the rest energy is given, not the mass.
In the lower part of column 2 of the table are given values of masses calculated by Wapstra \(^{7}\). In the opinion of specialists, these are the most accurate and best-agreed data among those available at present. We note that, with the exception of \((\mathrm{H}^{1})\), the values given are the masses of nuclei, not atoms.
For the deuteron, triton, and \(\mathrm{He}^{3}\) nuclei, the corresponding binding energies, B.E., are given in columns 3, 4.
Column 6
Here the known decay schemes of particles are given. Only for two particles, \(\pi^{0}\) and \(\Sigma^{+}\), is it known with certainty that they have more than one mode of decay \(^{\dagger}\). It is also customary to assume that the \(K_{\pi3}\)- or \(\tau'\)-particle is a \(\tau\)-meson decaying in two different ways.
\(\pi^{0}\). In addition to the usual decay into two photons, the decay of the neutral \(\pi^{0}\)-meson into a photon and an electron–positron pair is known. Such a decay occurs in one case out of eighty. Therefore one should expect that in every \((160)^{2}\) decays there will be one decay of \(\pi^{0}\) directly into two electron–positron pairs. There is evidence that such a decay was in fact observed in a Wilson chamber by Godson et al. \(^{10}\).
It has been shown that there exist hyperons with the following three decay schemes:
\[ \mathrm{Y}^{+} \to p + \pi^{0} + \sim 116\ \mathrm{MeV}, \]
\[ \mathrm{Y}^{+} \to n + \pi^{+} + \sim 110\ \mathrm{MeV}, \]
\[ \mathrm{Y}^{-} \to n + \pi^{-} + \sim 110\ \mathrm{MeV}. \]
The masses of these particles are close, thus, to \(2327\,m_e\), and it is tentatively assumed that these particles, called \(\Sigma\)-hyperons, are the positive and negative components of an isotopic spin triplet. This still requires confirmation (see the notes to column 8)\(\dagger\). In addition to the known decay schemes, for some particles possible or presumed schemes are also given in parentheses.
Column 7
The quantity \(Q\) in a given row denotes the total kinetic energy (measured in the rest system of the primary particle) of the secondary particles produced in the decay and indicated in the same row. This quantity is equal to the difference between the rest energy of the primary particle and the sum of the rest energies of the secondary particles.
\(\pi^\pm\). The values of \(Q\) for \(\pi^+\)- and \(\pi^-\)-mesons are given separately, although it seems to us that the value \(34.0 \pm 0.2\) MeV is probably the only value.
In those cases where the energies of secondary particles arising in the decay of \(K\)-mesons and hyperons are determined from their ranges in nuclear emulsions or multiplate Wilson chambers, this determination, in addition to other experimental errors, is affected by the inaccuracy in the range–energy relation. This inaccuracy is not included in the quoted errors.
Column 8
Column 8 gives the mean lifetime of each particle in seconds, unless another unit is indicated.
\(\vartheta^0\). The value given for the mean lifetime of \(\vartheta^0\) is the mean lifetime of all \(K\)-mesons observed in the experiments analyzed by Gaiser and Page\(^{12}\). It is assumed that the observed particles are mainly \(\vartheta^0\), but if there is a noticeable fraction of \(K^0\)-mesons of another type, the lifetime of \(\vartheta^0\) will be somewhat different\(\dagger\).
\(\Sigma^\pm\). It has not yet been clarified whether the \(\Sigma^+\)- and \(\Sigma^-\)-hyperons have identical mean lifetimes (and identical masses). According to the Gell-Mann and Pais scheme, for \(K\)-mesons and hyperons \(\Sigma^-\) is not the antiparticle of \(\Sigma^+\). Therefore one should not expect that the lifetimes (or masses) of these particles must necessarily prove to be identical. There is some evidence that the mean lifetime of \(\Sigma^-\) may be greater than \(3.4 \cdot 10^{-11}\) sec.
Columns 9, 11, 12 and 13
These columns contain data on the spin, parity, total isotopic spin \(T\) and its third, \(z\)-component \(T_z\), respectively. A discussion of these properties and the corresponding experimental
proofs can be found in the articles indicated in $^{3}$, as well as in the current literature.
Let us note that in column 9 the designations $Ц$ and $\dfrac{1}{2}Ц$ correspond to integral and half-integral spin. It is known that all particles with integral spin obey Bose–Einstein statistics, while all particles with half-integral spin obey Fermi–Dirac statistics.
Column 10
This column gives the measured magnetic moments of the particles. Let us note that in the upper part of the table the Bohr magneton is used as the unit, and in the lower part—the nuclear magneton.
Since the magnetic moments of the neutron, deuteron, triton, and the He$^{3}$ nucleus are measured relative to the proton, the errors in the values of these moments are conveniently expressed on the assumption that the error in the determination of the magnetic moment of the proton is equal to zero. This is how it has been done in this table. To obtain absolute errors, the errors given for these four particles must be combined in the appropriate manner with the error in the measurement of the magnetic moment of the proton.
Column 14
In this column, headed for brevity “Gell-Mann $S$,” are placed the values of a new quantum number which is possibly an intrinsic property of every type of particle. This number is often called the “strangeness” of the particle and is denoted by $S$. The use of the concept of “strangeness” (and of the corresponding selection rules) is explained by the fact that, thanks to this new quantum number, it has been possible qualitatively to bring into agreement the main known characteristics of the production, interaction, and decay of $K$-particles and hyperons and successfully to predict new properties. Similar ideas were expressed by other authors $^{17}$, and references $^{13}$ and $^{17}$ contain an incomplete list of works in this field. See also the discussion of the concept of “strangeness” in the works indicated in reference $^{3}$.
SECTION II
PARTICLES WHOSE PROPERTIES HAVE NOT BEEN DEFINITIVELY ESTABLISHED
All the particles in this section have been studied more or less thoroughly, and their existence has been quite reliably proved. The negative proton, or antiproton, is placed in this section because it has been discovered recently and many of its properties still
should be studied†. The \(K\)-particles are included in this section because it is still unclear which of the decays of these particles constitute competing decays of certain basic \(K\)-mesons. At present it is believed that there exist no more than two basic \(K\)-mesons, \(\tau\) and \(\vartheta\), but this still requires proof.
References to the literature are indicated by two small letters of the Latin alphabet.
A. NOTATION FOR \(K\)-PARTICLES
The \(K\)-particles of Section II are denoted first of all by the letter \(K\), followed by letter or numerical subscripts. All these particles decay into one charged and one or more neutral particles. The subscript 2 indicates that the decay occurs into two particles, i.e., that in addition to one charged particle only one neutral particle is formed; the subscript 3 indicates that not fewer than two neutral particles are emitted.
B. CONTENTS OF THE COLUMNS AND REMARKS
Columns 1 and 2
To the right of the designations \(K_{\pi2}\), \(K_{\pi3}\), and \(K_{\mu3}\) are given the Greek letters (\(\chi\), \(\tau'\), \(\varkappa\), respectively) by means of which these decay schemes are often denoted. By agreement¹ the Greek letters should not be used exclusively for denoting modes of decay; they should be reserved for “true” particles.
The second column contains the probable decay schemes. The first three of these have been established quite reliably, whereas the decay schemes of the last two particles are not yet completely clear. Below, in parentheses, possible competing decay schemes are indicated.
Column 3
Because of the scatter of the measured values of the \(K\)-particle masses, for each particle several mass values are given, obtained in the most recent and accurate experiments. For comparability, the errors quoted in all cases denote standard deviations. These errors are connected mainly with statistical inaccuracies. To the right of the errors are placed indices indicating the method of mass determination. Under the corresponding mass values given for each such \(K\)-particle are given the weighted mean (over all available measurements) and its standard deviation (followed by the designation “Av.”).
Column 4
Here are listed the mean lifetimes of the particles. The errors quoted denote standard deviations.
Columns 5, 6, 7, 8, and 9
These columns contain the decay value \(Q\), the kinetic energy \(E\), the momentum \(P\), the product of the momentum by \(\beta=v/c\), and the range \(R\) of the charged secondary particle, calculated under the assumption that the mass of the \(K\)-particle is equal to \(966m_e\) and that the particle decays after coming to rest into the secondary particles listed in column 2. These are calculated, not measured, values.
Column 10
In various experiments in which the properties of \(K\)-particles were investigated, it was shown that, independently of the method of production of the particles and of the experimental conditions, the relative fraction of particles decaying according to different schemes remains approximately the same. This ratio between the intensities of the different decay branches may prove to be a characteristic property of \(K\)-particles. It is given in column 10.
SECTION III
PARTICLES WHOSE EXISTENCE HAS BEEN ESTABLISHED LESS RELIABLY
1. \(\tau^0\) and other \(K^0\)-particles
It should be expected that, along with charged \(\tau\)-mesons, neutral \(\tau\)-mesons also exist. (The existence of \(\tau^0\)-mesons is predicted by the Gell-Mann “strangeness” scheme.) This meson may have one of the following, or both, decay schemes:
\[ \tau^0 \to \pi^+ + \pi^- + \pi^0, \]
\[ \tau^0 \to \pi^0 + \pi^0 + \pi^0. \]
It has often been pointed out that some (but not all) of the so-called anomalous \(V^0\)-decays may be examples of decay according to the first of these schemes. However, there is as yet insufficient evidence in favor of the existence of the \(\tau^0\)-meson. It may, generally speaking, also have other decay schemes.
Besides \(\vartheta^0\) and \(\tau^0\), other \(K^0\)-mesons may also exist. At present, however, it is customary to assume that there are no other neutral \(K\)-particles, but that other decay schemes of these two particles may exist. These other schemes may possibly explain some
which, among the remaining anomalous \(V^0\)-decays. Most such decays can be explained by the following schemes:
\[ K^0 \to \pi^+ + \pi^- + \gamma, \]
\[ K^0 \to \mu^\pm + \pi^\mp + \nu, \]
\[ K^0 \to e^\pm + \pi^\mp + \nu^\dagger . \]
2. \(\Sigma^0\) and \(\Xi^0\)
In addition to \(\Sigma^\pm\), a \(\Sigma^0\)-hyperon may also exist. It is predicted by those “strangeness” schemes \(^{13,17}\) in which the \(\Sigma\)-hyperons are assigned isotopic spin 1, and thus form a triplet. There is no direct proof of the existence of this particle, but some observations in a Wilson chamber \(^{20,21}\) testify in favor of such an assumption; from these it follows that, besides the formation process,
\[ \pi^- + p \to \Lambda^0 + \vartheta^0 \]
the existence of the process
\[ \pi^- + p \to \Sigma^0 + \vartheta^0, \]
is possible, with \(\Sigma^0\) rapidly decaying (mean lifetime \(\ll 10^{-10}\) sec) into \(\Lambda^0\) and a photon.
Experimental evidence for the existence of the \(\Xi^0\)-hyperon is lacking, but its existence also follows from the “strangeness” schemes \(^{13,17}\).
3. ANTINEUTRON AND OTHER ANTIPARTICLES
From the production of antiprotons at Berkeley \(^{22}\) it follows that the production of antineutrons is also possible. If Dirac’s theory is always applicable, then one may expect that every particle must have a corresponding antiparticle. Antiparticles must have the same properties as particles, except that the sign of the following properties must be replaced by the opposite one: charge, magnetic moment, the \(z\)-component of isotopic spin, the value \(S\), and the baryon number \(M\)*).
*) For example, the intense production of heavy unstable particles (\(K\)-mesons and hyperons) is permitted with conservation of the full value of \(S\) for the system (this occurs in pair production). The slow decay of these particles is a result of the fact that, in the decay, the value \(S\) must change by \(\pm 1\).
The relation between the magnitude of the charge of a particle \((q/|e|)\) and the \(z\)-component of its isotopic spin is given by the expression
\[ \left(\frac{q}{|e|}\right)=T_z+\frac{M}{2}+\frac{S}{2}, \]
where \(S\) is the number characterizing the “strangeness” of the particle, and \(M\) is the baryon number (\(M=+1\) for nucleons and hyperons, \(0\) for all light particles, and \(-1\) for antinucleons and antihyperons).
TABLE OF PROPERTIES OF ELEMENTARY PARTICLES (April 1956)
I. Particles whose existence has been reliably established
| Particle, designation and charge (1) | Mass \(\left(\dfrac{1}{16}O^{16}\right)^{a}\) (2) | Mass \((\mathrm{g})^{a}\) (3) | Mass \((m_e)\) (4) | Mass \((\mathrm{MeV})\) (5) | Secondary particles (6) | \(Q\) \((\mathrm{MeV})\) (7) | Mean lifetime, \((\mathrm{sec})\) (8) | Spin \((\hbar)\) (9) | Magnetic moment \(\left(\mu_0=\dfrac{e\hbar}{2m_e c}\right)\) (10) | Parity (11) | Isotopic spin \(T\) (12) | Isotopic spin \(T_z\) (13) | Gell-Mann \(S\) (14) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\gamma^0\) | \(0\) | \(0\) | \(0\) | \(0\) | Stable | \(0\) | \(\infty\) | \(1\) | \(<10^{-7}\,c\) | ||||
| \(\nu^0\) | \(<0.0005\) | \(<250\,\mathrm{eV}\) | Stable | \(0\) | \(\infty\) | \((1/2)\) | |||||||
| \(e^{-}\) | \(0.000548763\) (6) | \(9.1083\cdot10^{-28}\) (3) | \(1\) | \(0.510976\) (7) | Stable | \(0\) | \(\infty\) | \(1/2\) | \(-1.0011146\,d\) (12) | ||||
| \(e^{+}\) | Same mass as that of the electron to an accuracy of \(0.0071\%\) \(e\) | Same mass as that of the electron to an accuracy of \(0.0071\%\) \(e\) | Same mass as that of the electron to an accuracy of \(0.0071\%\) \(e\) | Same mass as that of the electron to an accuracy of \(0.0071\%\) \(e\) | \(e^{+}+e^{-}\to n\gamma\), \(n=2,3,\ldots\) | Positronium \({}^{3}S\): \(1.5\cdot10^{-7}\,f\) (15) | \(1/2\) | \((+1.001146)\) (12) | |||||
| \(L\)-mesons: \(\mu^{\pm}\) | \(\left\{\begin{array}{l}\text{Average }m_{\pi^\pm}=273.1\,m_e\\ \text{Average }m_{\pi^\pm}c^2=139.55\,\mathrm{MeV}\end{array}\right\}\) (1) | \(206.7\,g\) (2) | \(206.7\,g\) (2) | \(105.6\) (1) | \(e^{\pm}+\nu+\nu\) | \(105.1\) (1) | \(2.22\cdot10^{-6}\,h\) (2) | \((1/2)\) | |||||
| \(L\)-mesons: \(\pi^{+}\) | \(\left\{\begin{array}{l}\text{Average }m_{\pi^\pm}=273.1\,m_e\\ \text{Average }m_{\pi^\pm}c^2=139.55\,\mathrm{MeV}\end{array}\right\}\) (1) | \((273.3\,g)\) (2) | \((273.3\,g)\) (2) | \(139.7\) (1) | \(\mu^{+}+\nu\) | \(34.1\) (15) | \(2.53\cdot10^{-8}\,i\) (10) | \(0\) | \(-\) | \(1\) | \(+1\) | \((0)\) | |
| \(L\)-mesons: \(\pi^{-}\) | \(\left\{\begin{array}{l}\text{Average }m_{\pi^\pm}=273.1\,m_e\\ \text{Average }m_{\pi^\pm}c^2=139.55\,\mathrm{MeV}\end{array}\right\}\) (1) | \((272.8\,g)\) (3) | \((272.8\,g)\) (3) | \(139.1\) (15) | \(\mu^{-}+\nu\) | \(33.8\) (2) | \(2.55\cdot10^{-8}\,j\) (19) | \(0\) | \(-\) | \(1\) | \(-1\) | \((0)\) | |
| \(L\)-mesons: \(\pi^{0}\) | \(m_{\pi^-}-m_{\pi^0}=8.8\,m_e\,k\) (6) | \(264.3\) (7) | \(264.3\) (7) | \(135.0\) (3) | \(\gamma+\gamma\) \(\left(\dfrac{1}{80}\right)\); \(\gamma+e^{+}+e^{-}\) \(\left(\dfrac{1}{160?}\right)\); \(2e^{+}+2e^{-}\) | \(135.0\) (3) | \((1\text{–}5)\cdot10^{-15}\,l\) | \(0\) | \(-\) | \(1\) | \(0\) | \((0)\) |
| (1) Particle; charge designation | (2) Mass, $\left(\dfrac{1}{16}O^{16}\right)^d$ | (3) Mass, $(g)^a$ | (4) Mass, $(m_e)$ | (5) Mass, $(\mathrm{MeV})$ | (6) Secondary particles | (7) $Q$ $(\mathrm{MeV})$ | (8) Mean lifetime, $(\mathrm{sec})$ | (9) Spin, $(\hbar)$ | (10) Magnetic moment, $\left(\mu_0=\dfrac{e\hbar}{2Mpc}\right)$ | (11) Parity | (12) Isotopic spin $T$ | (13) Isotopic spin $T_z$ | (14) Strangeness $S$ |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| $K$-mesons; $\tau^+$ | $966.1$ (2) | $493.7$ (1) | $\pi^+ + \pi^+ + \pi^-$ $(\pi^+ + \pi^0 + \pi^0)$ |
$75.0\,m$ (8) | (12) $1.27\cdot 10^{-8}\ n$ (2) |
$(0)^m$ | $(-)^m$ | $\left(+\dfrac{1}{2}\right)$ | $(+1)$ | ||||
| $K$-mesons; $\tau^-$ | $(966.1)$ (2) | $(493.7)$ (1) | $\pi^- + \pi^+ + \pi^-$ $(\pi^- + \pi^0 + \pi^0)$ |
$(75.0)$ (8) | (12) $(1.27\cdot 10^{-8})$ (2) |
$(0)$ | $(--)$ | $\left(-\dfrac{1}{2}\right)$ | $(-1)$ | ||||
| $K$-mesons; $\theta^0$ | $965$ (10) | $493$ (5) | $\pi^+ + \pi^-$ $(\pi^0 + \pi^0)$ |
$214^\circ$ (5) | (4) $1.3\cdot 10^{-10}\ p$ (3) |
[[unclear: symbol]] $\ne 1$ | $(+?)$ | $\left(-\dfrac{1}{2}\right)$ | $(+1)$ | ||||
| Nucleons; atomic mass units | $1.000000$ | $931.141^d$ (10) | |||||||||||
| Nucleons; $p^+$ | $1.0075964$ (15) | $1.67239\cdot 10^{-24}$ (4) | $1836.12$ (2) | $938.214$ (10) | Stable | $\infty$ | $\dfrac{1}{2}$ | $+2.792743\ r$ (3) | $\dfrac{1}{2}$ | $+\dfrac{1}{2}$ | $(0)$ | ||
| Nucleons; $n^0$ | $1.0089861$ (15) | $1.67470\cdot 10^{-24}$ (4) | $1838.65$ (2) | $939.508$ (10) | $p^+ + e^- + \nu$ | $0.7830\ q$ (9) | $1.11\cdot 10^3\ s$ (22) $T^{1/2}=12.8$ min |
$\dfrac{1}{2}$ | $-1.913138\ r$ (44) | $\dfrac{1}{2}$ | $-\dfrac{1}{2}$ | $(0)$ | |
| Nucleons; $(\mathrm{H}^1)'$ | $1.0081452$ (15) |
Continuation
| Particle, designation and charge | Mass \(\left(-\dfrac{1}{16}O^{16}\right)^a\) | Mass \((e)^a\) | Mass \((m_e)\) | Mass (MeV) | Secondary particles | \(Q\) (MeV) | Mean lifetime, sec | Spin \((\hbar)\) | Magnetic moment \(\left(\mu_0=\dfrac{e\hbar}{2M_pc}\right)\) | Parity | Isotopic spin \(T\) | Isotopic spin \(T_z\) | Strangeness \(S\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Hyperons: \(\Lambda^0\) | \(2181,5\) \((2)\) |
\(1114,7\) \((1)\) |
\(p^+ + \pi^-\) \((n^0+\pi^0)\) |
\(36,9\,t\) \((1)\) |
(b) \(3,7\cdot10^{-10}\) and \((5)\) |
\(\dfrac{1}{2}\) | \((0)\) | \((-1)\) | |||||
| Hyperons: \(\Sigma^+\) | \(2326,9\) \((3)\) |
\(1189,0\) \((1,5)\) |
\(p^+ + \pi^0\) \(n^0+\pi^+\) |
\(115,8\,v,w\) \((1)\) \(109,9\) \((1)\) |
\((1,4)\) \((\sim)3,4\cdot10^{-11}\,w,x\) \((8)\) |
\(\dfrac{1}{2}\) | \((+1)\) | \((-1)\) | |||||
| Hyperons: \(\Sigma^-\) | \((2326,9)\) \((3)\) |
\(1189,0\) \((1,5)\) |
\(n^0+\pi^-\) | \((109,9)\) \((1)\) |
\((1,4)\) \((\geq)3,4\cdot10^{-11}\) \((8)\) |
\(\dfrac{1}{2}\) | \((-1)\) | \((-1)\) | |||||
| Hyperons: \(\Xi^-\) | \(2586\) \((7)\) |
\(1321\) \((3,5)\) |
\(\Lambda^0+\pi^-\) | \(67\,y\) \((3)\) |
\(\sim1\cdot10^{-10}\,x\) | \(\dfrac{1}{2}\) | \(\left(-\dfrac{1}{2}\right)\) | \((-2)\) | |||||
| \((\mathrm H^2)^+\) | \(2,0141915\) \((28)\) |
M.D. \(=-2,2264\) \((18)\) |
\(1875,496\) \((14)\) |
Stable | \(1\) | \(+0,8574073\,r\) \((2)\) |
\(+\) | \(0\) | \(0\) | ||||
| \((\mathrm H^3)^+\) | \(3,016456\) \((5)\) |
M.D. \(=-8,458\) \((4)\) |
\(2808,746\) \((17)\) |
\(\mathrm{He}^{3+++}+e^-+\nu\) | \(0,0181\,q\) \((2)\) |
\(17,690\) \((6)\) hours |
\(\dfrac{1}{2}\) | \(+2,97884\,r\) \((1)\) |
\(\dfrac{1}{2}\) | \(-\dfrac{1}{2}\) | |||
| \((\mathrm{He}^3)^{+++}\) | \(3,015888\) \((5)\) |
M.D. \(=-7,720\) \((4)\) |
\(2808,217\) \((17)\) |
Stable | \(\dfrac{1}{2}\) | \(-2,127544\,r\) \((7)\) |
\(\dfrac{1}{2}\) | \(+\dfrac{1}{2}\) |
II. Particles whose properties have not been finally established
| Particle, designation and charge (1) | Probable secondary particles (2) | Measured mass \((m_e)\) (3) | Mean lifetime (sec) (4) | If mass is \(966\,m_e\): \(Q\) (Mev) (5) | If mass is \(966\,m_e\): \(E\) of charged secondary (Mev) (6) | If mass is \(966\,m_e\): \(p\) of charged secondary (Mev/c) (7) | If mass is \(966\,m_e\): \(p^{*}\) of charged secondary (Mev/c) (8) | If mass is \(966\,m_e\): \(R\) of charged secondary \((\mathrm{g}/\mathrm{cm}^2\,\mathrm{Pb})\) (9) | Observed fraction of \(K^{+}\)-decays (10) |
|---|---|---|---|---|---|---|---|---|---|
| \(K_{\pi2}^{(\pm)} \equiv \tau_{1}^{(\pm)} \equiv = \vartheta^{(\pm)}?\) | \(\pi^{(\pm)}+\pi^{0}\) | \(964\pm4^{*}\) aa \(967\pm2^{\dagger}\) bb \(968\pm3^{*}\) cc \(964\pm2^{*}\) bb \(\overline{966\pm2}\) Cp |
\(12.1^{+1.1}_{-1.0}\times10^{-9}\) ff \(\sim10\cdot10^{-9}\) aa |
219.1 | 108.5 | 205.1 | 169.6 | 60 | \(\sim0.27\) |
| \(K_{\pi3}^{(\pm)} \equiv \tau'^{(\pm)} \equiv =(\tau^{(\pm)}?)\) | \(\pi^{(\pm)}+\pi^{0}+\pi^{0}\) | \(968\pm8^{\dagger}\) aa \(952\pm16^{\dagger}\) dd \(\overline{965\pm7}\) Cp |
\(\sim10\cdot10^{-9}\) aa | 84.1 | \(\leq53.1\) | \(\leq132.9\) | \(\leq91.6\) | \(\leq21.2\) | \(\sim0.02\) |
| \(K_{\mu2}^{(\pm)}\) | \(\mu^{(\pm)}+\nu\) | \(964\pm6^{*}\) aa \(976\pm7^{*}\) cc \(965\pm3^{*}\) bb \(968\pm2^{\dagger}\) bb \(\overline{966\pm2}\) Cp |
\(11.7^{+0.8}_{-0.7}\times10^{-9}\) ff \(\sim10\cdot10^{-9}\) aa |
388.0 | 152.5 | 235.5 | 214.9 | 106 | \(\sim0.57\) |
| \(K_{\mu3}^{(\pm)}\equiv\kappa^{(\pm)}\) | \(\mu^{(\pm)}+\pi^{0}+\nu\) \((\mu^{(\pm)}+\gamma+\nu)\) |
\(956\pm9^{\dagger}\) aa \(951\pm15^{\dagger}\) dd \(967\pm6^{\dagger}\) bb \(\overline{964\pm5}\) Cp |
\(\sim10\cdot10^{-9}\) aa | 253.0 | \(\leq134.0\) | \(\leq215.1\) | \(\leq193.1\) | \(\leq91\) | \(\sim0.04\) |
| \(K_{e3}^{(\pm)}\) | \(e^{(\pm)}+?+?\) \((e^{(\pm)}+\pi^{0}+\nu)\) \((e^{(\pm)}+\gamma+\nu)\) |
\(984\pm25^{\dagger}\) aa \(988\pm40\) ee \(963\pm10^{\dagger}\) bb \(\overline{967\pm9}\) Cp |
\(\sim10\cdot10^{-9}\) aa | \(\sim0.04\) Remaining part of decays, \(\sim0.06\), belongs to \(\tau\)-mesons |
|||||
| \(P^{-}\) | Same mass as for \(p^{+}\), to an accuracy of \(\pm5\%\) gg |
4. HEAVIER HYPERONS
It is possible that there exist hyperons heavier than the \(\Xi^-\). Eisenberg observed an event that may be interpreted as an argument in favor of the existence of such particles. For the observed event the assumed decay scheme has the form
\[ Y^- \to K^- + (n \ \text{or} \ \Lambda^0) + (Q = 5\ \text{MeV}). \]
The sign of this particle was obtained on the basis that the stopped \(K\)-meson is absorbed by the emulsion nucleus and forms a large star.
Fry, Schneps, and Swami\({}^{24}\) also found an event which indicates the existence of heavier hyperons.
5. OTHER “ANOMALOUS” PARTICLES OR DECAY SCHEMES
Other events have been found which do not fit into the data given in the table and in the text. It is impossible to list them all, and we mention the most important. Such are the apparently existing group of negatively charged particles, evidently \(K\)-particles, which have a considerably shorter lifetime than the “normal” \(K\)-particles\({}^{25}\).
Notes in proof. The following notes are a consequence of information obtained at the Sixth Annual Rochester Conference (April 1956). A full discussion of these data may be found in the proceedings of the conference, which will be published. See also Waschington Meeting Bulletin of the American Physical Society (ser. II, vol. 1, April 1956).
-
There is some evidence for the existence, among negative \(K\)-mesons, of \(K_{\pi2}^-\), \(K_{e3}^-\), and, possibly, \(K_{\pi3}^-\) and \(K_{\mu2}^-\) particles.
-
In addition to the \(\pi^0\)-, \(\Sigma^+\)-, and \(\tau\)-particles, it now seems necessary that the \(\vartheta^0\)- and \(\Lambda^0\)-particles have additional decay schemes in which only neutral secondary particles arise. This is necessary if all “strange” particles (i.e., particles with \(S \ne 0\)) are produced in pair production and if there are no new strange particles.
-
Some experiments indicate that the \(\Sigma^-\)-hyperon is approximately \(14\)–\(16\) electron masses heavier than the \(\Sigma^+\), and that the mean lifetime of the \(\Sigma^-\) is \(\sim 1.4 \cdot 10^{-10}\) sec, which is considerably greater than that of the \(\Sigma^+\). This does not prevent both hyperons from belonging to one isotopic triplet.
-
Some recent experiments give for the mean lifetime of the \(\vartheta^0\)-meson a value smaller than that given in the table. The new mean value is approximately \(1.0 \cdot 10^{-10}\) sec.
-
The equality of the masses of the proton and antiproton has now been established with an accuracy of \(\sim 2\%\).
- Several cases have been observed indicating the probable existence of the following decay scheme:
\[ K^0 \to e^{\pm} + \pi^{\mp} + (\text{light neutral particle}). \]
-
Additional evidence has been obtained for the existence of the \(\Sigma^0\)-hyperon. It seems very probable that this particle exists and that its properties fit into the strangeness scheme.
-
At present it is assumed that the group of negatively charged particles with mean lifetimes of the order of \(10^{-10}\) sec consists rather of \(\Sigma^-\)-hyperons than of \(K^-\)-mesons.
CITED LITERATURE
-
Amaldi, Anderson, Blackett, Fretter, LePrince-Ringuet, Peters, Powell, Rochester, Rossi and Thompson, Nature 173, 123 (1954); Nuovo cimento 11, 213 (1954).
-
Recently many good tables have been published. The basic arrangement of this table is analogous to that adopted in an earlier table compiled by Prof. B. Rossi. Notes to the proofreader. A table of mesons and hyperons was recently published by M. M. Shapiro [Am. J. Phys. 24, 196 (1956)]. This work contains a complete bibliography of the literature up to the middle of 1955.
-
See, for example, the summaries prepared independently by R. E. Marshak and R. V. Thompson at the International Conference of 1955 in Pisa (unpublished); Mimeographed Proceedings of the International Conference on Elementary Particles, Pisa, June, 1955 [Nuovo cimento (to be published)]; Part I, Session 3 of the Varenna Lectures, Nuovo cimento, Suppl. No. 1, 2, 163—274 (1955); Proceedings of the Fifth Annual Rochester Conference, 1955 (Interscience Publishers, Inc., New York, 1955); Proceedings of the 1954 Glasgow Conference on Nuclear and Meson Physics (Pergamon Press, London and New York, 1955); various reviews appearing in the volumes The Annual Review of Nuclear Science, Progress in Cosmic Ray Physics, and the Reports on Progress in Physics.
-
Smith, Birnbaum and Barkas, Phys. Rev. 91, 765 (1955).
-
Barkas, Birnbaum and Smith, Phys. Rev. 101, 778 (1956).
-
K. M. Crowe and R. H. Phillips, Phys. Rev. 96, 470 (1954).
-
A. H. Wapstra, Physica 21, 367 (1955).
-
Lindenfeld, Sachs and Steinberger, Phys. Rev. 89, 521 (1953).
-
R. H. Dalitz, Proc. Phys. Soc. (London) A64, 667 (1955).
-
Hodson, Ballam, Arnold, Harris, Rau, Reynolds and Treiman, Phys. Rev. 96, 1089 (1954).
-
D. B. Gayther, Phil. Mag. 45, 570 (1954); 46, 1362 (1955).
-
D. I. Page, Phil. Mag. 46, 103 (1955).
-
M. Gell-Mann and A. Pais, Proceedings of the 1954 Glasgow Conference on Nuclear and Meson Physics (Pergamon Press, London, 1955).
-
Schneps, Swami, Fry and Snow, Bull. Am. Phys. Soc. Ser. 11, 1, 64 (1956).
15, 16. M. Gell-Mann, Lectures at Massachusetts Institute of Technology and Harvard, 1955 (unpublished).
- A. Pais, Physica 19, 869 (1953); M. Gell-Mann, Phys. Rev. 92, 833 (1953); Nuovo cimento (to be published); T. Nakano and K. Nishi-
jima, Progr. Theoret. Phys. (Japan) 10, 581 (1953); M. Goldhaber, Phys. Rev. 92, 1297 (1953); 101, 433 (1956); D. C. Peaslee, Nuovo cimento 12, 943 (1954); J. Rayski, Nuovo cimento 12, 945 (1954); R. G. Sachs, Phys. Rev. 99, 1573 (1955).
-
See, for example, the review by Thompson R. V. at the Pisa Conference of 1955: R. W. Thompson, Progress in Cosmic Ray Physics, edited by J. G. Wilson (to be published), vol. 3, and other works cited in reference 3.
-
See, for example, Ballam, Grisaru and Treiman, Phys. Rev. 101, 1438 (1956).
-
Fowler, Shutt, Thorndike and Whittemore, Phys. Rev. 98, 121 (1955).
-
W. D. Walker, Phys. Rev. 98, 1407 (1955).
-
Chamberlain, Segrè, Wiegand and Ypsilantis, Phys. Rev. 100, 947 (1955).
-
Y. Eisenberg, Phys. Rev. 96, 541 (1954); Mimeographed Proceedings of the International Conference on Elementary Particles, Pisa, June, 1955 [Nuovo cimento (to be published)].
-
Fry, Schneps and Swami, Phys. Rev. 97, 1189 (1955); Nuovo cimento 2, 346 (1955).
-
See, for example, reference 3 and G. H. Trilling and R. B. Leighton, Phys. Rev. 100, 1468 (1955).
LITERATURE FOR THE TABLES
a) Cohen, DuMond, Layton, and Rollett, Revs. Modern Phys. 27, 363 (1955).
b) L. M. Langer and R. J. Moffat, Phys. Rev. 88, 689 (1952).
c) Cowan, Reines and Harrison, Phys. Rev. 96, 1294 (1954).
d) Koenig, Prodell and Kusch, Phys. Rev. 88, 191 (1952).
e) Page, Stehle and Gunst, Phys. Rev. 89, 1273 (1953).
f) M. Deutsch, Phys. Rev. 83, 866 (1951).
g) Smith, Birnbaum, and Barkas, Phys. Rev. 91, 765 (1953); Barkas, Birnbaum, and Smith, Phys. Rev. 101, 778 (1956).
h) W. E. Bell and E. P. Hincks, Phys. Rev. 84, 1243 (1951).
i) Jakobson, Schultz and Steinberger, Phys. Rev. 81, 894 (1951); W. L. Kraushaar, Phys. Rev. 86, 513 (1952).
j) Durbin, Loar and Havens, Phys. Rev. 88, 179 (1952).
k) W. Chitinowsky and J. Steinberger, Phys. Rev. 93, 586 (1954).
l) D. H. Perkins, Phil. Mag. 46, 1146 (1955); B. M. Anand, Proc. Roy. Soc. (London) A220, 183 (1953).
m) E. Amaldi, Report on $\tau$ Mesons, Mimeographed Proceedings of the Pisa Conference on Elementary Particles, June, 1955, Nuovo cimento (to be published); H. H. Heckman, Nuovo cimento (to be published).
n) L. Alvarez and S. Goldhaber, Nuovo cimento 2, 344 (1955); Harris, Orear and Taylor, Phys. Rev. 100, 932 (1955). V. Fitch, New York Meeting of the American Physical Society, February 1, 1956 (unpublished).
o) Thompson, Burwell, Cohn, Huggett and Karzmark, Phys. Rev. 95, 661 (1954).
p) D. I. Page, Phil. Mag. 46, 103 (1955); D. B. Gayther, Phil. Mag. 45, 570 (1954); 46, 1362 (1955).
q) Li, Whaling, Fowler and Lauritsen, Phys. Rev. 83, 512 (1951); K. T. Bainbridge, Experimental Nuclear Physics, edited by E. Segré (John Wiley and Sons, Inc., New York, 1953), vol. I; R. W. King, Revs. Modern Phys. 26, 327 (1954); D. M. Van Patter and W. Whaling, Revs. Modern Phys. 26, 402 (1954); Duckworth, Hogg and Pennington, Revs. Modern Phys. 26, 463 (1954); A. H. Wapstra, Physica 21, 367 (1955).
r) N. F. Ramsey, Molecular Beams, Oxford University Press, New York, 1956.
s) J. M. Robson, Phys. Rev. 83, 349 (1951).
t) C. C. Butler, Report on Hyperons, Mimeographed Proceedings of the Pisa Conference on Elementary Particles, June, 1955.
u) D. I. Page, Phil. Mag. 45, 863 (1954).
v) Friedlander, Keefe and Menon, Nuovo cimento 1, 482 (1955); Baldo, Belliboni, Ceccarelli, Grille, Sechi, Vitale and Zorn, Nuovo cimento 1, 1180 (1955).
w) Schneps, Swami, Fry and Snow, Bull. Am. Phys. Soc., Ser. II, 1, 64 (1956).
x) Davies, Evans, Fowler, Francois, Friedlander, Hiller, Iredale, Keefe, Menon, Perkins and Powell, Mimeographed Proceedings of the Pisa Conference on Elementary Particles, June, 1955; Dahanayake, Francois, Fujimoto, Iredale, Waddington and Yasin, Nuovo cimento 1, 888 (1955).
y) Castagnoli, Cortini and Manfredini, Nuovo cimento 2, 565 (1955).
z) W. M. Jones, Phys. Rev. 100, 124 (1955).
* Obtained from the measurement of \(Q\)-decay.
† Obtained from comparison of the range of \(K\)-particles with the range of protons having the same momentum.
‡ Obtained from comparison of the range of \(K\)-particles with the range of \(\tau\)-mesons having the same momentum, under the assumption that the mass of the \(\tau\)-meson is equal to \(966\,m_e\).
aa) Ritson, Pevsner, Fung, Widgoff, Zorn, Goldhaber and Goldhaber, Phys. Rev. 101, 1085 (1956).
bb) Whitehead, Stork, Peterson, Perkins and Birge, UCRL—3295 (March, 1956) (unpublished).
cc) G-Stack Collaboration, Nuovo cimento 2, 1063 (1955).
dd) Heckman, Smith and Barkas, UCRL—3156 (October, 1955), (unpublished); Nuovo cimento 3, 85 (1956).
ee) H. H. Heckman, UCRL—3003 (May, 1955) (unpublished).
ff) V. Fitch and R. Motley, Phys. Rev. 101, 496 (1956).
gg) Chamberlain, Segré, Wiegand and Ypsilantis, Phys. Rev. 100, 947 (1955).