Behind the Picture: RFK's Assassination, Los Angeles, 1968

May 15, 2014 4:55 PM EDT

How many times must we live through these throat-paralyzing sequences of days of gun play, grief and muffled drums?

That question, posed by LIFE magazine in its June 14, 1968, issue, is freighted with all of the emotions — sorrow, frustration, a kind of bewildered dread — unleashed by the events that unsettled the country in the first half of that schizoid year. The assassination of Dr. King; the Tet Offensive, the My Lai massacre and the other horrors of the war in Vietnam; and, on June 5, the murder of Robert Kennedy by a Jerusalem-born Palestinian Christian, Sirhan Sirhan, in the kitchen of the Ambassador Hotel in Los Angeles.

Here, remembering RFK’s assassination — a murder made, if possible, all the more heinous by the fact that Kennedy was gunned down just as he was finding his true voice as the leader of a vast, disaffected cross-section of the American public — LIFE.com presents a series of photos by the great Bill Eppridge. Many of the photos featured here never ran in LIFE.

The very first picture in the gallery is, of course, not only the most recognized and most frequently reproduced picture from that night, but one of the most chilling, signature images of the 1960s. As a historical document, it’s indispensable. As a photograph, it’s astonishing: made in an instant, Eppridge’s picture possesses the immediacy of great photojournalism, while somehow conveying the totemic sense — especially in its interplay of (barely perceptible) light and (profound) dark — one sometimes encounters in portraits by the Old Masters.

Rembrandt himself, one imagines, might have felt a kinship with the tone, the lighting, the bleak intensity of the scene.

The nation in less than six years [LIFE wrote] has watched the violent deaths of two Kennedys and a King. If Robert Kennedy, a complex man, ambitious and fatalistic, did not inspire so universal an admiration as his brother, he had shown himself capable of growing and deepening. He died too young; the Kennedy family has paid dearly or its ardor for public service.

Almost instinctive in the recoil at his murder was the sense that it was a part of a climate of violence. Arthur Schlesinger [JFK’s “court historian”] may have been speaking more in the moment than as a historian when he said last week “we are today the most frightening people on this planet.” Even if he is a Pasadena resident, a Jordanian Arab [RFK’s assassin, Sirhan] who kills out of a hatred for his ancient enemy, the Jews, may be a better example of classic Middle Eastern methods than of the callous kook our mixed-media society is accused of turning on and turning loose.

President Johnson was right when he said, “Two hundred million Americans did not strike down Robert Kennedy. . . .” But it is surely a good thing to ask ourselves whether the compulsion to violence was born entirely within a killer or whether we and our society are somehow accomplices. . . . The Vietnam war has been our most vivid daily exposure to violence — and the nation’s eagerness to stop it comes less from any political reappraisal of the ends than a moral revulsion at the means: we don’t love violence all that much.

In the decades since LIFE expressed those sentiments, millions of words have been written about the Kennedys and, specifically, about the abiding intensity with which Lyndon Johnson and Robert Kennedy despised one another. The two men had been enemies — not too strong a word — ever since Johnson accepted JFK’s invitation to be his running mate, a decision Bobby Kennedy vocally fought until, and beyond, the 1960 Democratic convention. But in early June 1968, it was still possible for most Americans to believe that President Johnson might, in fact, genuinely mourn the loss of the dynamic — if chimerical and often arrogant — Robert Kennedy.

The photographs that Bill Eppridge made before, during and after RFK’s assassination don’t require that we forget all we’ve learned about the dank underside of American politics in order to appreciate the fear, rage and anguish sparked by Kennedy’s death. On the contrary, the pictures in this gallery suggest that despite how ambitious and even cruel he could sometimes be, Bobby Kennedy obviously inspired, in countless people, the better angels of their nature.

(One person whose better angels were clearly not stirred was Sirhan Sirhan, who murdered Bobby Kennedy because Kennedy supported Israel; or maybe because he, Sirhan, was drunk and murderously furious on the one-year anniversary of the beginning of the Six-Day War in the Middle East; or perhaps, as he later claimed, because he was brainwashed . . . take your pick. Sirhan’s stated reasons for pumping three bullets into Bobby Kennedy — and injuring several other people that night — have varied wildly through the years.)

Would Robert Kennedy have won the Democratic nomination if Sirhan had not gunned him down in that hotel kitchen? Would he have gone on to beat Richard Nixon in the general election if he had won the nomination? Playing “What if. . . . ?” is always an intriguing, if ultimately pointless, exercise. The real measure of the man has to be taken not by what he might have done, but by what he actually said and what he did during his lifetime.

“A complex man, ambitious and fatalistic,” LIFE wrote of Kennedy, a man who had “shown himself capable of growing and deepening.” We’ll never know how much he might have grown, how much further he might have deepened, had Sirhan’s bullets not silenced him. In the end, that’s where much of the tragedy of the tale lies: in the ruined promise of a dead man’s unmeasured potential.

Robert Kennedy was 42 when he was killed. He and his wife, Ethel, had 11 children; the last, Rory, was born six months after the assassination. In the decades since RFK’s death, two of those children, David and Michael, have died.

Sirhan Sirhan is now 70 years old, and serving a life sentence in a California prison. He has a parole hearing every five years.

Ben Cosgrove is the Editor of LIFE.com